Question

# A particle is found to be at rest when seen from a frame S1 and moving with a constant velocity when seen from another frame S2. Mark out the possible options.

A

Both the frames are inertial.

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B

Both the frames are non-inertial.

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C

is inertial and is non-inertial.

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D

is non-inertial and is inertial.

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Solution

## The correct options are A Both the frames are inertial. B Both the frames are non-inertial. lets assume that frame S1 has velocity v and acceleration a. Then particle P will also have velocity v and acceleration a As P is at rest with respect to S1 VPS2=VP−VS2=V−V=0 aPS2=aP−aS2=a−a=0 Now it's mentioned that the particle P has a constant velocity with respect to S2 (frame 2) ⇒VPS2 = VP−VS2 = V - 2v = - V aPS2=0 (since constant velocity) =aP−aS2=0 ⇒a−aS2=0 ⇒aS2=a This proves that both the frames have same acceleration so if aS1=0 ⇒aS2=0 So both are inertial but if aS1=a then aS2=a so both will be non- inertial. What you should understand is that given such a scenario, either both the frames are non-inertial or both the frames are inertial. One can't be inertial if the other is non-inertial.

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