Question

# A particle stays at rest as seen in a frame. We can conclude that

A

the frame is inertial

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B

resultant force on the particle is zero

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C

the frame is inertial if the resultant force on the particle is zero

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D

The frame is non-inertial if there is a non-zero resultant force.

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Solution

## The correct options are C the frame is inertial if the resultant force on the particle is zero D The frame is non-inertial if there is a non-zero resultant force. Imagine a block is kept on the seat next to you on a train. Outside everything is dark you can't see anything. Now lets check every option. (a) The frame is inertial. Well if you can't look outside and you have no way of figuring out the acceleration of the train then you cannot simply say whether you are at rest or are you moving with constant velocity or constant acceleration etc........ So the block may very well be at rest with respect to you in the train but you can't surely say if the train's frame is inertial or not (b) If the train is at rest or moving with constant velocity then Free Body Diagram of block. If the train is moving with a constant acceleration with respect to an inertial frame then Free Body Diagram of block So again just by looking you can't claim. (c) But if we know that the resultant force on the block is 0 and we know its at rest then surely we can say the body is in an inertial frame (d) Now if I tell you that net resultant force is not zero on the block. But you see the object is at rest with respect to you. This means that the frame is non-inertial.

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