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Question

A stone dropped from the window of a stationary train hits the ground and comes to rest. An identical stone is dropped from the window when the same train is moving with speed v and it comes to rest on the ground. Assume that in each case, the entire energy lost in impact goes into heating the stone. Then:

A
The first stone is slightly more heated than the second
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B
The second stone is slightly more heated than the first
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C
Both the stones will be raised to the same temperature
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D
The second stone will be slightly more heated than the first only if its horizontal speed during fall is more than the final vertical speed
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Solution

The correct option is B The second stone is slightly more heated than the first
When stone A is dropped it has only potential energy mgh, when it reaches the ground.
That energy is given by,
Energy=mgh (1)

When second particle is dropped from moving train then it has both potential energy and kinetic energy and is given by,
Energy=mgh+12mv2 (2)
v= velocity of particle when dropped from moving train with speed v

So, energy is more in second case and it goes into heating the stone.
Therefore second stone is more heated than the first.




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