Question

A particle is observed from two frames $S_{1}and{S}_2$. The frame $S_2$ moves with respect to $S_1$ with an acceleration a. Let $F_{1}and{F}_2$ be the pseudo forces on the particle when seen from $S_{1}and{S}_2$ respectively. Which of the following are not possible?

• A. $F_1=0,F_2\ne 0$
• B. $F_1\ne 0,F_2=0$
• C. $F_1\ne 0,F_2\ne 0$
• D. $F_1=0,F_2=0$

Answer 1

The correct option is D

$F_1=0,F_2=0$

Let us assume there a two frames $S_{1}and{S}_2$ moving with acceleration $a_{1}and{a}_2$. Now we know (a1−a2) = a as relative acceleration is a.

Now, magnitude of pseudo forces $F_{1}and{F}_2$ will be ma₁ and ma₂ irrespective of where the object is.

$F_1=m{a}_1$, $F_2=m{a}_2$

when $a_1=0,then{F}_1=0,F_2\ne 0$

$a_2=0,then{F}_1\ne 0,F_2=0$

$when,a_1\ne 0,a_2\ne 0then,F_1\ne 0,F_2\ne 0$

but it is impossible for both $F_1=0and{F}_2=0$ as for this to happen, $a_1=0and{a}_2=0$ which is not the case as there is relative acceleration.