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A man inside a freely falling box throws...

A man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friciton. Which of the following figures depicts the motion of the centre of mass of the entire system (man, the ball and the box)?

A

B

C

D

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the motion of the center of mass of the entire system, which consists of the man, the ball, and the box, as they fall freely under the influence of gravity. ### Step-by-Step Solution: 1. **Understanding the System**: - We have a man inside a box that is falling freely. The man throws a heavy ball towards one of the walls of the box. - The entire system (man + ball + box) is in free fall, meaning they are all accelerating downwards at the same rate due to gravity. 2. **Identifying Forces**: - The only external force acting on the entire system is the gravitational force (mg), where m is the total mass of the system (man + box + ball) and g is the acceleration due to gravity. - Since there are no other external forces acting on the system (we neglect air resistance and friction), the motion of the center of mass will be influenced solely by this gravitational force. 3. **Motion of the Center of Mass**: - In a freely falling system, the center of mass of the system will also fall freely under the influence of gravity. - The center of mass will move downward with the same acceleration as the rest of the system, which is g (acceleration due to gravity). 4. **Bouncing of the Ball**: - While the ball bounces between the walls of the box, the horizontal motion does not affect the vertical motion of the center of mass. - The center of mass will continue to move downward as the ball bounces back and forth, but there will be no net horizontal movement of the center of mass since the forces acting in the horizontal direction are internal to the system. 5. **Conclusion**: - Therefore, the motion of the center of mass of the entire system will be a downward motion, and it will not move horizontally. - The correct depiction of the motion of the center of mass is that it moves straight down. ### Final Answer: The center of mass of the entire system (man, ball, and box) will move downward.
To solve the problem, we need to analyze the motion of the center of mass of the entire system, which consists of the man, the ball, and the box, as they fall freely under the influence of gravity. ### Step-by-Step Solution: 1. **Understanding the System**: - We have a man inside a box that is falling freely. The man throws a heavy ball towards one of the walls of the box. - The entire system (man + ball + box) is in free fall, meaning they are all accelerating downwards at the same rate due to gravity. ...
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