A particle is observed from two frames $S_{1} a n d S_{2}$ . The frame $S_{2}$ moves with respect to $S_{1}$ with an acceleration a. Let $F_{1} a n d F_{2}$ be the pseudo forces on the particle when seen from $S_{1} a n d S_{2}$ respectively. Which of the following are not possible?

$F_{1} = 0, F_{2} \neq 0$

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$F_{1} \neq 0, F_{2} = 0$

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$F_{1} \neq 0, F_{2} \neq 0$

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$F_{1} = 0, F_{2} = 0$

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Solution

The correct option is D
$F_{1} = 0, F_{2} = 0$

Let us assume there a two frames $S_{1} a n d S_{2}$ moving with acceleration $a_{1} a n d a_{2}$ . Now we know (a1−a2) = a as relative acceleration is a.

Now, magnitude of pseudo forces $F_{1} a n d F_{2}$ will be ma₁ and ma₂ irrespective of where the object is.

$F_{1} = m a_{1}$ , $F_{2} = m a_{2}$

when $a_{1} = 0, t h e n F_{1} = 0, F_{2} \neq 0$

$a_{2} = 0, t h e n F_{1} \neq 0, F_{2} = 0$

$w h e n, a_{1} \neq 0, a_{2} \neq 0 t h e n, F_{1} \neq 0, F_{2} \neq 0$

but it is impossible for both $F_{1} = 0 a n d F_{2} = 0$ as for this to happen, $a_{1} = 0 a n d a_{2} = 0$ which is not the case as there is relative acceleration.

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