Initially the spring is underformed. Now the force 'F' is applied to 'B' as shown in the figure. When the displacement of 'B' w.r.t. 'A' is 'x' towards right in some time, then the relative acceleration of 'B' w.r.t. 'A' at that moment is:

\frac{F}{2 m}

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\frac{F - k x}{m}

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\frac{F - 2 k x}{m}

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None of these

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Solution

The correct option is C $\frac{F - 2 k x}{m}$
At the instant suggested in the problem, the spring is elongated by $x$ and the spring force is $k x$ .
So,
$F - k x = m b$
and $k x = m a$

Hence ,
$m (b - a) = F - 2 k x$
Ans(c).

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