Question

# Rajat is sitting in an open cart that moves horizontally with an acceleration of 5 m/s2 rightwards. Rajat is unaware of his acceleration, and throws a ball up in the air. He attempts at drawing a Free Body Diagram of the ball assuming his frame to be inertial. Which of these would closely resemble his free body diagram of the ball (neglect air drag)?

A

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B

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C

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D

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Solution

## The correct option is B So Rajat saw that the ball is falling down with g as the experiment is happening on ground so there will be a gravitational pull of mg downwards. Also with respect to him the ball has an acceleration of 5 m/s2 leftward. But how can there be acceleration without a force. Rajat's belief is that he is in an inertial frame (which isn't true) he knows physics. He knows if there is acceleration then there will be force. So he just assumes a force on the ball in the leftward direction. This force is a pseudo force as its not real. According to him this pseudo force will be responsible for the pseudo (unreal) acceleration of the block. So F = ma (pseudo force) F = (m×5)N Note: Actually in ground (inertial) frame the ball is just falling down under gravity so Free Body Diagram will have only one force. While in cart (non-inertial) frame ball has a pseudo (unreal) acceleration with respect to cart's frame so a pseudo force which is equal to mass × acceleration of frame and direction opposite to the acceleration of frame will be applied.

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