The accelerations of a particle as seen from two frames S_1 and S… - Vidyadip

MCQ

The accelerations of a particle as seen from two frames $S_1$ and $S_2$ have equal magnitude $4 \mathrm{~m} / \mathrm{s}^2$.

A
The frames must be at rest with respect to each other.
B
The frames may be moving with respect to each other but neither should be accelerated with respect to the other.
C
The acceleration of $\mathrm{S}_2$ with respect to $\mathrm{S}_1$ may either be zero or $8 \mathrm{~m} / \mathrm{s}^2$.
✓
The acceleration of $S_2$ with respect to $S_1$ may be anything between zero and $8 \mathrm{~m} / \mathrm{s}$.

✓

Answer

Correct option: D.

The acceleration of $S_2$ with respect to $S_1$ may be anything between zero and $8 \mathrm{~m} / \mathrm{s}$.

$\overrightarrow{\text{a}}_{\text{s}_2\text{s}_1}=\overrightarrow{\text{a}}_{\text{s}_2\text{P}}+\overrightarrow{\text{a}}_{\text{Ps}_1}$
$\big|\overrightarrow{\text{a}}_{\text{s}_2\text{s}_1}|=\sqrt{4^2+4^2+32\cos(\theta)}$
$-1<\cos(\theta)<1$
$0<\overrightarrow{\text{a}}_{\text{s}_2\text{s}_1}<8$

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