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 is either 0 or $4m/s^2$.
• B. Their relative acceleration may have any value between 0 and $4m/s^2$.
• C. Both of the frames may be stationary with respect to 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 0 and $4m/s^2$.
C Both of the frames may be stationary with respect to earth.
D The frames may be moving with same acceleration in same direction.

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