A particle is observed from two frames S₁ and S₂. Frame S₂ moves with respect to S₁ with an acceleration a. Let F₁and F₂ be the pseudo forces on the particle when seen from S₁ and S₂, respectively. Which of the following is not possible?
(a) F₁ = 0, F₂ ≠ 0
(b) F₁ ≠ 0, F₂ = 0
(c) F₁ ≠ 0, F₂ ≠ 0
(d) F₁ = 0, F₂ = 0

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Solution

(d) F₁ = 0, F₂ = 0

$a_{s_{2} s_{1}} = a . . . (1)$
Acceleration of the particle w.r.t. to S₁ = F₁/m
Acceleration of the particle w.r.t. to S₂ = F₂/m
If we assume F₁ = 0 and F₂ = 0,
we can conclude that $a_{s_{2} s_{1}} = 0 . . . (2)$
From equations (1) and (2), we can say that our assumption is wrong.
And F₁ = 0, F₂ = 0 is not possible.

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