Question

A particle is found to be at rest when seen from a frame $S_1$ and moving with a constant velocity when seen from another frame $S_2$. Mark out the possible options.

• A. Both the frames are inertial.
• B. Both the frames are non-inertial.
• C. $S_1$ is inertial and $S_2$ is non-inertial.
• D. $S_1$ is non-inertial and $S_2$ is inertial.

Answer 1

Answer: (A), (B)

Both the frames are non-inertial.

lets assume that frame $S_1$ 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 $S_1$

$V_{P{S}_2}=V_P-V_{S_2}=V-V=0$

$a_{P{S}_2}=a_P-a_{S_2}=a-a=0$

Now it's mentioned that the particle P has a constant velocity with respect to $S_2$ (frame 2)

$\Rightarrow V_{P{S}_2}$ = $V_P-V_{S_2}$

= V - 2v

= - V

$a_{P{S}_2}=0$ (since constant velocity)

$=a_P-a_{S_2}=0$

$\Rightarrow a-a_{S_2}=0$

$\Rightarrow a_{S_2}=a$

This proves that both the frames have same acceleration so if $a_{S_1}=0$

$\Rightarrow a_{S_2}=0$

So both are inertial

but if $a_{S_1}=athen{a}_{S_2}=a$ 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.