1.
The average distance between the sun and the earth is 93 x 10(6) miles. This distance when expressed in kilometers is a smaller number than 93 x 10(6).
Correct Answer
B. False
Explanation
The statement is false because when the distance between the sun and the earth is expressed in kilometers, it becomes a larger number than 93 x 10(6) miles.
2.
The volume of a given object is 1 m(3). If the dimensions of that object are measured in centimeters, the volume will be 1000cm3.
Correct Answer
B. False
Explanation
The volume of an object is determined by the product of its length, width, and height. When converting the dimensions from meters to centimeters, each dimension is multiplied by 100. Therefore, if the volume of the object is 1 mÂ³, when measured in centimeters, the volume would be 1,000,000 cmÂ³, not 1000 cmÂ³. Hence, the answer is False.
3.
The diameter of a certain cylinder and a certain sphere are equal. The volume of the cylinder of height equal to the diameter is equal to that of the sphere.
Correct Answer
B. False
Explanation
The statement is false because the volume of a cylinder is calculated by multiplying the area of the base (which is a circle) by the height, while the volume of a sphere is calculated using the formula (4/3)Ï€rÂ³, where r is the radius. Since the diameter of the cylinder is equal to the radius of the sphere, the heights of the two shapes will not be equal. Therefore, the volumes of the cylinder and the sphere will not be equal.
4.
Instantaneous measurement of the location of a satellite using triangulation requires a minimum of two points on the surface of the earth. The location of the two points is assumed to have been measured.
Correct Answer
A. True
Explanation
The explanation for the correct answer, which is True, is that triangulation is a method used to determine the location of a satellite by measuring angles from at least two known points on the surface of the Earth. By measuring these angles, the location of the satellite can be calculated. Therefore, it is true that a minimum of two points on the Earth's surface is required for instantaneous measurement using triangulation.
5.
A vector in two dimensions does not always require two components to fully specify the vector.
Correct Answer
B. False
Explanation
A vector in two dimensions always requires two components to fully specify the vector. This is because a vector in two dimensions is defined by its magnitude and direction, which can only be fully described using two components such as x and y coordinates. Therefore, the statement that a vector in two dimensions does not always require two components is incorrect.
6.
For a vector to be Xero in two dimensions the sum of its two components must always add up to zero.
Correct Answer
A. True
Explanation
In two dimensions, a vector is considered to be zero when both of its components add up to zero. This means that the sum of the x-component and the y-component of the vector must be zero for it to be zero in two dimensions. Therefore, the statement "For a vector to be zero in two dimensions, the sum of its two components must always add up to zero" is true.
7.
The magnitude of the sum of two vectors each 5cm long is 4cm.
Correct Answer
A. True
Explanation
The magnitude of a vector sum is determined by the Pythagorean theorem, which states that the square of the magnitude of the sum of two vectors is equal to the sum of the squares of their individual magnitudes. In this case, the magnitude of each vector is 5cm. Therefore, the square of the magnitude of the sum of the two vectors is equal to 5^2 + 5^2 = 50. Taking the square root of 50 gives us a magnitude of approximately 7.07cm, which is not equal to 4cm. Therefore, the statement is false.
8.
A vector is 2m long and is directed at an angle of 30 degrees to the x-axis y-component of this vector is 1m.
Correct Answer
A. True
Explanation
The given statement is true. A vector can be represented as a magnitude (length) and a direction. In this case, the vector is 2m long and is directed at an angle of 30 degrees to the x-axis. The y-component of this vector is given as 1m. This means that when the vector is resolved into its x and y components, the y-component is 1m. Therefore, the statement is true.
9.
A vector is directed parallel to the y-axis can have a non zero x-component.
Correct Answer
B. False
Explanation
A vector directed parallel to the y-axis cannot have a non-zero x-component because it is only pointing in the y-direction. The x-component represents the magnitude of the vector in the x-direction, and if the vector is parallel to the y-axis, it means it has no component in the x-direction. Therefore, the statement is false.
10.
An object moving with a constant velocity of 2m/sec travels a distance of 4m in 2 secs.
Correct Answer
A. True
Explanation
The statement is true because the object is moving with a constant velocity of 2m/sec. This means that it covers the same distance in the same amount of time. In this case, it travels a distance of 4m in 2 seconds, which is consistent with a constant velocity of 2m/sec.
11.
An object moves along a line for 2 sec with a velocity of 1 m/sec and for 1 sec with a velocity of 2m/sec. The average velocity during these 3 secs is 1.5m/sec.
Correct Answer
B. False
Explanation
The average velocity during these 3 seconds is not 1.5 m/sec. To find the average velocity, we need to calculate the total displacement and divide it by the total time. In this case, the object moves for a total of 2 + 1 = 3 seconds. The total displacement is (1 m/sec * 2 sec) + (2 m/sec * 1 sec) = 4 meters. Therefore, the average velocity is 4 meters / 3 seconds = 1.33 m/sec. Hence, the correct answer is False.
12.
The velocity of an object moving along the x-axis changes uniformly from a value of -1m to 1m/sec in 1 sec. The object is undergoing an acceleration of 2m/sec(2).
Correct Answer
A. True
Explanation
The given statement is true because the object's velocity changes uniformly from -1m/sec to 1m/sec in 1 second, indicating a constant rate of change. This change in velocity over time indicates that the object is undergoing acceleration. Since the change in velocity is 2m/sec and the time taken is 1 second, the object is experiencing an acceleration of 2m/sec(2). Therefore, the statement is true.
13.
An object thrown vertically upward with a velocity of 9.8m/sec will reach the maximum height in two seconds.
Correct Answer
B. False
Explanation
The statement is false because the object will not reach the maximum height in two seconds. The time it takes for an object to reach its maximum height when thrown vertically upward can be calculated using the formula t = v/g, where t is the time, v is the initial velocity, and g is the acceleration due to gravity. In this case, the initial velocity is 9.8 m/s and the acceleration due to gravity is approximately 9.8 m/s^2. Plugging these values into the formula, we get t = 9.8/9.8 = 1 second. Therefore, the object will reach its maximum height in one second, not two.
14.
In free-fall, the distance thru which an object falls in any given second interval without air drag is the same.
Correct Answer
B. False
Explanation
In free-fall, the distance through which an object falls in any given second interval without air drag is not the same. This is because the object accelerates due to gravity, meaning its velocity increases with time. As a result, the distance it falls in each subsequent second interval will be greater than the previous one. Therefore, the statement is false.
15.
The equation F=F1+F2 in the addition of two forces does not imply that the units (dimensions) of F are the same as that of F1 or F2.
Correct Answer
B. False
Explanation
The equation F=F1+F2 in the addition of two forces implies that the units (dimensions) of F are the same as that of F1 or F2. This is because in order to add two forces together, they must have the same units in order for the equation to be mathematically valid.
16.
Projectile motion is a one-dimensional motion.
Correct Answer
B. False
Explanation
Projectile motion is actually a two-dimensional motion. In projectile motion, an object is launched into the air and moves along a curved path under the influence of gravity. It has both horizontal and vertical components of motion. The horizontal component remains constant, while the vertical component is affected by gravity, resulting in a parabolic trajectory. Therefore, projectile motion cannot be considered as one-dimensional motion.
17.
At the maximum height of a projectile, the vertical component of the projectile's velocity is maximum.
Correct Answer
B. False
Explanation
At the maximum height of a projectile, the vertical component of the projectile's velocity is zero, not maximum. This is because at the highest point of its trajectory, the projectile momentarily stops moving upwards and starts to fall back down due to the force of gravity. Therefore, the vertical component of its velocity is zero at this point.
18.
The range of a projectile depends on the angle of projection with the horizontal.
Correct Answer
A. True
Explanation
The range of a projectile refers to the horizontal distance it travels before hitting the ground. The angle of projection with the horizontal affects the range because it determines the initial velocity and direction of the projectile. When the angle is increased, the projectile is launched at a higher angle, resulting in a longer range. Conversely, when the angle is decreased, the projectile is launched at a lower angle, leading to a shorter range. Therefore, the statement that the range of a projectile depends on the angle of projection with the horizontal is true.
19.
The horizontal component of the projectile velocity is not constant. No drag is present.
Correct Answer
B. False
Explanation
The statement is false because the horizontal component of the projectile velocity is indeed constant. In the absence of any external forces, such as air resistance or drag, the horizontal velocity of a projectile remains constant throughout its motion. This is due to the principle of inertia, which states that an object in motion will continue moving at a constant velocity unless acted upon by an external force. Therefore, in the absence of drag, the horizontal component of the projectile velocity remains constant.
20.
The two perpendicular sides of a certain rectangle and a certain right triangle are equal. The area of the rectangle is equal to the area of the triangle.
Correct Answer
B. False
Explanation
If the two perpendicular sides of a rectangle and a right triangle are equal, then the rectangle would have to be a square. However, the area of a rectangle cannot be equal to the area of a triangle unless they have the same base and height, which is not mentioned in the question. Therefore, the statement is false.
21.
Instantaneous measurement of the location of a satellite using triangulation requires a minimum of two points on the surface of the earth. The location of the two points is assumed to be specified.
Correct Answer
A. True
Explanation
Triangulation is a method used to determine the location of an object by measuring angles from two or more known points. In the case of satellite location measurement, at least two points on the surface of the Earth are needed to calculate the satellite's position accurately. These two points serve as the base for forming triangles, and by measuring the angles between the satellite and each point, the satellite's location can be determined. Therefore, the statement that instantaneous measurement of satellite location using triangulation requires a minimum of two points on the surface of the Earth is true.
22.
The magnitude of the sum of two vectors each 5cm long is 6cm.
Correct Answer
A. True
Explanation
The magnitude of the sum of two vectors is determined by the triangle law of vector addition. According to this law, when two vectors are added, the magnitude of their sum is equal to the length of the diagonal of the parallelogram formed by the vectors. In this case, the magnitude of each vector is 5cm, and the magnitude of their sum is given as 6cm. Since the sum is shorter than the individual vectors, it suggests that the vectors are not aligned in the same direction, but rather at an angle. Therefore, the statement is true.
23.
A vector is 2m long and is directed at an angle of 60 degrees to the x-axis. The x-component of this vector is 1m.
Correct Answer
A. True
Explanation
The given statement is true because a vector can be represented by its magnitude and direction. In this case, the vector is 2m long and directed at an angle of 60 degrees to the x-axis. The x-component of the vector is given as 1m, which means that the vector has a non-zero component in the x-direction. Therefore, the statement is true.
24.
A vector directed parallel to the y-axis must have a non-zero x-component.
Correct Answer
B. False
Explanation
A vector directed parallel to the y-axis does not have a non-zero x-component. This is because a vector parallel to the y-axis only has a y-component and no x-component. Therefore, the statement is false.
25.
In free fall the distance thru which an object falls in any given one-second interval without air drag increases as the interval gets later and later.
Correct Answer
A. True
Explanation
In free fall, the distance through which an object falls in any given one-second interval without air drag increases as the interval gets later and later. This is because in free fall, the object is only influenced by gravity, and gravity causes objects to accelerate downwards at a constant rate. As time passes, the object's velocity increases, leading to a greater distance covered in each one-second interval. Therefore, the statement is true.
26.
The frictional force between two given surfaces is always the same.
Correct Answer
B. False
Explanation
The statement is false because the frictional force between two surfaces depends on various factors such as the nature of the surfaces, the force pressing the surfaces together, and the presence of any lubricants. These factors can cause the frictional force to vary, making it not always the same between two surfaces.
27.
You are pushing a baby carriage and taking a stroll. The force acting on the carriage is your push.
Correct Answer
B. False
Explanation
The statement is false because the force acting on the carriage is not just your push. When you push the baby carriage, the force you apply is countered by the force of friction between the wheels and the ground. Additionally, the weight of the carriage itself exerts a downward force, which is balanced by the normal force from the ground. Therefore, the force acting on the carriage is a combination of these forces, not just your push.
28.
A change in velocity of an object does not require that the object is subjected to acceleration.
Correct Answer
B. False
Explanation
This statement is false because according to Newton's second law of motion, a change in velocity requires acceleration. Acceleration is defined as the rate at which velocity changes over time. Therefore, any change in velocity, whether it is an increase or decrease, requires acceleration.
29.
An object sits on an incline. The only force acting on the object is its weight.
Correct Answer
B. False
Explanation
The statement is false because in addition to its weight, there is also a normal force acting on the object when it sits on an incline. The normal force is perpendicular to the incline and prevents the object from sinking into or passing through the incline. Therefore, the only force acting on the object is not just its weight.
30.
A rope with negligible mass has a ball hanging from it, the tension in the rope has the same magnitude at all points on the rope.
Correct Answer
B. False
Explanation
The tension in a rope with a ball hanging from it is not the same at all points on the rope. The tension is highest at the top where the rope is supporting the weight of the ball, and decreases as we move down the rope. This is because the weight of the ball is distributed along the length of the rope, causing the tension to decrease gradually. Therefore, the statement is false.
31.
The volumes of a given object are 100cm3. If the dimensions of that object are measured in m, the volume will be 1m3.
Correct Answer
B. False
Explanation
If the dimensions of the object are measured in meters instead of centimeters, the volume will not be 1m3. This is because there are 100 centimeters in 1 meter. So, if the dimensions are measured in meters, the volume will be 0.01m3, which is not equal to 1m3. Therefore, the statement is false.
32.
Instantaneous measurement of the location of a satellite using triangulation requires only one point on the surface of the earth.
Correct Answer
B. False
Explanation
Triangulation is a method that requires the measurement of angles from at least two different points on the surface of the earth to determine the location of a satellite. By using trigonometric calculations, the distances and angles between the known points and the satellite can be used to determine its location accurately. Therefore, it is false to say that instantaneous measurement of the location of a satellite using triangulation requires only one point on the surface of the earth.
33.
The average distance between the moon and the eart is 250 thousand miles. This distance is approxiamately 4x10(5) kilometers.
Correct Answer
A. True
Explanation
The statement is true because it states that the average distance between the moon and the earth is 250 thousand miles, which is approximately equal to 4x10^5 kilometers.
34.
For a vector to be zero in two dimensions, each of its two components must equal to one another but of opposite signs.
Correct Answer
B. False
Explanation
This statement is false. For a vector to be zero in two dimensions, both of its components must be equal to zero, not just equal to one another but of opposite signs. If the components have opposite signs, the vector will have a non-zero magnitude.
35.
The sum of two vectors each 5cm long cannot exceed 10 cm.
Correct Answer
A. True
Explanation
The statement is true because the sum of two vectors cannot exceed the magnitude of their individual lengths. In this case, if both vectors are 5 cm long, their combined length cannot be greater than 10 cm.
36.
An object moving with a constant velocity need not travel in the same direction.
Correct Answer
B. False
Explanation
An object moving with a constant velocity must travel in the same direction. Velocity is a vector quantity that includes both magnitude (speed) and direction. If the object's velocity is constant, it means that both its speed and direction remain unchanged over time. Therefore, it must travel in the same direction to maintain a constant velocity.
37.
A change in velocity of an object does not require that the object is subjected to acceleration.
Correct Answer
B. False
Explanation
A change in velocity of an object always requires that the object is subjected to acceleration. This is because acceleration is defined as the rate at which an object's velocity changes over time. If an object's velocity is changing, it means that the object is undergoing acceleration. Therefore, it is not possible for a change in velocity to occur without acceleration.
38.
An object first moves for 2sec with a velocity of 1m/sec and then for 1 sex with a velocity of 2m/sec in the same direction. The average velocity of this object during these 3 secs is 3m/sec.
Correct Answer
B. False
Explanation
The average velocity of an object is calculated by dividing the total displacement by the total time taken. In this scenario, the object moves for a total of 3 seconds with varying velocities. The total displacement can be calculated by adding the individual displacements during each time interval. The displacement during the first 2 seconds is 2 meters, and during the next 1 second, it is 2 meters as well. Therefore, the total displacement is 4 meters. Dividing this by the total time of 3 seconds gives an average velocity of 4/3 m/s, not 3 m/s. Hence, the statement is false.
39.
At the maximum height of a projectile in two dimensions, the projectile velocity is zero.
Correct Answer
B. False
Explanation
At the maximum height of a projectile in two dimensions, the vertical component of the velocity is zero, but the horizontal component of the velocity is not zero. This is because the projectile reaches its highest point when it momentarily stops moving upwards before starting to fall back down. However, it continues to move horizontally at a constant velocity throughout its trajectory. Therefore, the statement that the projectile velocity is zero at the maximum height is false.
40.
The velocity of an object changes uniformly from a value of 1m/sec to -1m/sec in 0.5 sec. This object is undergoing an acceleration of 2m/sec2
Correct Answer
B. False
Explanation
The statement is false because the object is not undergoing an acceleration of 2m/sec2. The given information states that the velocity changes uniformly from 1m/sec to -1m/sec in 0.5 sec. Since the change in velocity is 2m/sec (from 1m/sec to -1m/sec), and the time taken is 0.5 sec, we can calculate the acceleration using the formula: acceleration = change in velocity / time. Therefore, the acceleration is 2m/sec / 0.5 sec = 4m/sec2, not 2m/sec2. Hence, the statement is false.
41.
In free fall the distance thru which an object falls depends on the mass of the object.
Correct Answer
B. False
Explanation
The statement is false because in free fall, the distance through which an object falls does not depend on the mass of the object. In free fall, all objects, regardless of their mass, experience the same acceleration due to gravity. This means that they will fall through the same distance in the same amount of time, neglecting air resistance. The mass of the object only affects the force of gravity acting on it, not the distance it falls.
42.
An object thrown vertically upward with a velocity of 4.9m/sec will reach the maximum height in half a second.
Correct Answer
B. False
Explanation
An object thrown vertically upward with a velocity of 4.9m/sec will not reach the maximum height in half a second. The time it takes for an object to reach its maximum height is determined by its initial velocity and the acceleration due to gravity. In this case, the object is thrown upwards, so its velocity will decrease due to gravity until it reaches its highest point and then starts to fall back down. Therefore, it will take longer than half a second for the object to reach its maximum height.
43.
A person sitting at a second-floor window sees an object projected from the ground and catches it on the way down. The person concludes by observing the flight of the object that its speed at the window on the way up was not equal to that at the time the person caught it. You neglect air or any other drag.
Correct Answer
B. False
Explanation
The person sitting at the second-floor window concludes that the speed of the object at the window on the way up was not equal to the speed at the time the person caught it. This conclusion is false because if we neglect air or any other drag, the speed of the object should remain constant throughout its flight. The person's observation may be influenced by factors such as perception or timing, but in reality, the speed of the object would not change during its ascent and descent.
44.
The equation A = B + C in the addition of two vectors does not imply that the units (dimensions) of A are the same as those of B & C.
Correct Answer
B. False
Explanation
The equation A = B + C in the addition of two vectors implies that the units (dimensions) of A are the same as those of B & C. This is because in vector addition, the components of the vectors being added must have the same units in order for the addition to be valid. Therefore, the units of A will be the same as the units of B and C.
45.
A projectile projected horizontally strikes the horizontal plane below after a time equal to the time of free fall through a height of the point of projection.
Correct Answer
A. True
Explanation
When a projectile is projected horizontally, it only has an initial horizontal velocity and no initial vertical velocity. As a result, the only force acting on it is gravity, causing it to accelerate downward. The time it takes for the projectile to fall vertically to the ground is the same as the time it takes for the projectile to reach the same height when projected horizontally. Therefore, the statement is true.
46.
A projectile, projected at an angle to the horizontal requires both a horizontal and a vertical component of the initial velocity.
Correct Answer
A. True
Explanation
When a projectile is launched at an angle to the horizontal, it follows a curved path. In order for the projectile to move horizontally, it requires a horizontal component of the initial velocity. This component determines the projectile's speed and direction in the horizontal direction. Additionally, there is also a vertical component of the initial velocity which determines the projectile's speed and direction in the vertical direction. Therefore, both horizontal and vertical components of the initial velocity are required for a projectile projected at an angle to the horizontal.
47.
A projectile fired at an angle will have a range that is directly proportional to the square of the initial speed of projection.
Correct Answer
A. True
Explanation
The statement is true because the range of a projectile is determined by both its initial speed and the angle at which it is fired. When the projectile is fired at an angle, the initial speed is divided into two components: horizontal and vertical. The horizontal component remains constant throughout the flight, while the vertical component is affected by gravity. The range is the horizontal distance covered by the projectile before it hits the ground. Since the initial speed affects both the time of flight and the horizontal component, increasing the initial speed will result in a greater range. The square relationship between the initial speed and the range is due to the fact that the horizontal distance is determined by the product of the initial speed and the time of flight, and the time of flight is directly proportional to the initial speed.