Question

The acceleration of a particle as observed from two different frames $S_1$ and $S_2$ have equal magnitudes of 2$m{s}^{-2}$

• A. The relative acceleration of the frame may either be zero or 4 $m{s}^{-2}$
• B. Their relative acceleration may have any value between zero to 4 $m{s}^{-2}$
• C. Both the frames may be stationary with respect to the earth
• D. The frames may be moving with same acceleration in same direction

Answer 1

Answer: (B), (C), (D)

The correct options are
B Their relative acceleration may have any value between zero to 4 $m{s}^{-2}$
C Both the frames may be stationary with respect to the earth
D The frames may be moving with same acceleration in same direction

Acceleration of particle w.r.t frame $S_1:{\overrightarrow{a}}_p-{\overrightarrow{a}}_{s_1}=2\hat{n}$

Acceleration of particle w.r.t frame $S_2:{\overrightarrow{a}}_p-{\overrightarrow{a}}_{s_2}=2\hat{m}$

Where $\hat{m}$ and $\hat{n}$ are unit vectors in any direction. Now relative acceleration of frames:

${\overrightarrow{a}}_{s_2}-{\overrightarrow{a}}_{s_1}=2(\hat{n}-\hat{m})$

Its magnitude can have any value between 0 to 4 $m{s}^{-2}$, depending upon the direction of $\hat{m}and\hat{n}$