Physics - Mechanics Final Test

1. A boy throws a ball vertically upwards as shown. What is the displacement of the ball when it returns to its starting point?

0 m

5 m

5 m upwards then 5 m downwards

10 m

When the ball is thrown vertically upwards, it gains potential energy as it moves against gravity. However, when it reaches its peak and starts to fall back down, it loses the same amount of potential energy and gains the same amount of kinetic energy. This means that when the ball returns to its starting point, its displacement is zero, as it has returned to the same position it started from.

Explanation

When the ball is thrown vertically upwards, it gains potential energy as it moves against gravity. However, when it reaches its peak and starts to fall back down, it loses the same amount of potential energy and gains the same amount of kinetic energy. This means that when the ball returns to its starting point, its displacement is zero, as it has returned to the same position it started from.

2. In the following figure, a ball runs on a smooth rail from P to Q.

Which of the following graphs best represents the variation of the distance d travelled by the ball with time t?

Graph A

Graph B

Graph C

Graph D

not-available-via-ai

Explanation

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3. Balls A and B are thrown vertically upwards and downwards respectively.

If their initial speeds are the same, which of the following statements is/are correct when they meet? (1) Their displacements should be the same. (2) Their speeds should be the same. (3) Their accelerations should be the same.

(1) only

(3) only

(1) and (3) only

When balls A and B meet, it means that they are at the same height. Since ball A is thrown vertically upwards and ball B is thrown vertically downwards, their displacements should not be the same. However, their accelerations should be the same because they are both under the influence of gravity. Therefore, the correct statement is that their accelerations should be the same.

Explanation

When balls A and B meet, it means that they are at the same height. Since ball A is thrown vertically upwards and ball B is thrown vertically downwards, their displacements should not be the same. However, their accelerations should be the same because they are both under the influence of gravity. Therefore, the correct statement is that their accelerations should be the same.

4. The following graph shows that quantity X is directly proportional to time t.

Which of the following can be the quantity X? (1) Velocity of a freely falling object with negligible air resistance. (2) Displacement of an object moving at constant velocity. (3) Distance travelled by an object moving with constant acceleration.

(1) and (2) only

(1) and (3) only

(2) and (3) only

(1), (2) and (3)

The graph shows that quantity X is directly proportional to time t, which means that as time increases, quantity X also increases. This relationship is seen in both options (1) and (2). In option (1), the velocity of a freely falling object with negligible air resistance will increase as time increases. In option (2), the displacement of an object moving at constant velocity will also increase as time increases. Therefore, both options (1) and (2) can be the quantity X. Option (3), the distance travelled by an object moving with constant acceleration, does not show a direct proportionality with time, so it is not a possible quantity X.

Explanation

The graph shows that quantity X is directly proportional to time t, which means that as time increases, quantity X also increases. This relationship is seen in both options (1) and (2). In option (1), the velocity of a freely falling object with negligible air resistance will increase as time increases. In option (2), the displacement of an object moving at constant velocity will also increase as time increases. Therefore, both options (1) and (2) can be the quantity X. Option (3), the distance travelled by an object moving with constant acceleration, does not show a direct proportionality with time, so it is not a possible quantity X.

5. In the figure below, a cannon-ball has been fired from a cannon

Which of the following figures best shows the direction of the resultant force acting on the cannon-ball at different time?

Picture A

Picture B

Picture C

Picture D

Picture A best shows the direction of the resultant force acting on the cannon-ball at different times because it depicts the cannon-ball moving in a parabolic trajectory, indicating that it is subject to both horizontal and vertical forces. This suggests that there is a combination of both forward and upward forces acting on the cannon-ball, which would result in a parabolic path. Picture B, C, and D do not accurately represent the motion of a cannon-ball being fired from a cannon.

Explanation

Picture A best shows the direction of the resultant force acting on the cannon-ball at different times because it depicts the cannon-ball moving in a parabolic trajectory, indicating that it is subject to both horizontal and vertical forces. This suggests that there is a combination of both forward and upward forces acting on the cannon-ball, which would result in a parabolic path. Picture B, C, and D do not accurately represent the motion of a cannon-ball being fired from a cannon.

6. Using a stop-watch, Tom measured the time for a motor car to pass through 2 streetlights. The reading was 1.2 s. If the reaction time of Tom is 0.2 s, what is the maximum possible percentage error of his measurement?

8.33%

16.7%

33.3%

66.7%

Tom measured the time for a motor car to pass through 2 streetlights using a stop-watch. The reading was 1.2 s. However, Tom's reaction time is 0.2 s, which means there is an inherent delay in his starting and stopping the stop-watch. This reaction time introduces an error in his measurement. The maximum possible percentage error can be calculated by dividing the reaction time by the measured time and multiplying by 100. In this case, (0.2 s / 1.2 s) * 100 = 16.7%. Therefore, the correct answer is 16.7%.

Explanation

Tom measured the time for a motor car to pass through 2 streetlights using a stop-watch. The reading was 1.2 s. However, Tom's reaction time is 0.2 s, which means there is an inherent delay in his starting and stopping the stop-watch. This reaction time introduces an error in his measurement. The maximum possible percentage error can be calculated by dividing the reaction time by the measured time and multiplying by 100. In this case, (0.2 s / 1.2 s) * 100 = 16.7%. Therefore, the correct answer is 16.7%.