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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=VPVS2=VV=0

aPS2=aPaS2=aa=0

Now it's mentioned that the particle P has a constant velocity with respect to S2 (frame 2)

VPS2 = VPVS2

= V - 2v

= - V

aPS2=0 (since constant velocity)

=aPaS2=0

aaS2=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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