Mechanical Engineering Trivia Quiz

The potential energy of a vertically raised body is equal to the kinetic energy of a vertically falling body. This is because as the raised body falls, its potential energy is converted into kinetic energy. The total energy remains constant, so the potential energy lost by the raised body is equal to the kinetic energy gained by the falling body. Therefore, the potential energy and kinetic energy are equal.

The centre of gravity is the point in a body where the entire weight of the body can be considered to act. It is the point where the body is in perfect balance and if suspended from this point, it will remain stable in any position. The centre of gravity is independent of the body's position and is determined by the distribution of mass within the body.

Newton's second law of motion states that the rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction in which the force acts. This law explains the relationship between force, mass, and acceleration. It states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

The mechanical advantage in ideal machines is equal to the velocity ratio. This means that the force gained or lost in an ideal machine is equal to the distance gained or lost. In other words, the mechanical advantage is the ratio of the output force to the input force, and the velocity ratio is the ratio of the output distance to the input distance. In ideal machines, these two ratios are equal, resulting in a mechanical advantage that is equal to the velocity ratio.

Speed is a scalar quantity because it only represents the magnitude of motion, i.e., how fast an object is moving, without any consideration of direction. Scalar quantities are described solely by their magnitude. For example, if a car is traveling at 60 miles per hour, its speed is 60 mph, and this information does not include any information about the direction in which the car is moving. In contrast, velocity, which is a vector quantity, includes both magnitude (speed) and direction. Therefore, speed is not a vector quantity, making it the correct answer to the question.

The angular velocity of a body rotating at N revolutions per minute can be calculated using the formula 2πN/60. This formula takes into account the number of revolutions (N) and converts it into radians per second by multiplying it by 2π and dividing it by 60. This conversion is necessary because angular velocity is measured in radians per second, while revolutions per minute is a unit of rotational speed.

The minimum force required to slide a body of weight W on a rough horizontal plane is equal to the force of friction between the body and the surface. This force of friction can be calculated using the following formula:

Frictional Force (F_friction)=Coefficient of Friction (μ)×Normal Force (N)

Where:

Coefficient of Friction (μ) is a dimensionless constant that depends on the nature of the surfaces in contact (static or kinetic friction). Normal Force (N) is the force exerted by the surface perpendicular to the direction of motion and is equal to the weight of the body (W) in this case. So, the minimum force required to slide the body is determined by the coefficient of friction and the weight of the body.

The moment of inertia of an object is a measure of its resistance to changes in rotational motion. For a square of side a, the moment of inertia about its diagonal can be calculated using the parallel axis theorem. The diagonal of a square divides it into two congruent right triangles. The moment of inertia of each triangle about its base is (1/12) * base^3, where the base is the side length of the square. Since there are two congruent triangles, the total moment of inertia about the diagonal is (2 * (1/12) * a^3) = a^3/6. However, the moment of inertia is a property of mass distribution, so it is divided by the mass of the square to get the moment of inertia per unit mass. Since the mass of the square is a^2, the moment of inertia per unit mass is (a^3/6) / (a^2) = a/6. Therefore, the moment of inertia of the square about its diagonal is a/6.

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