On applying a force $F$ , point $P$ is displaced vertically down by 'y' from equilibrium position. Find the applied force $F$ in terms of 'y' if the point $A$ is displaced by $\frac{y}{2}$ due to application of $F$ .

k y

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\frac{k y}{2}

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\frac{k y}{4}

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2 k y

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Solution

The correct option is C $\frac{k y}{4}$
The given arrangement can be simply converted to the string system as shown
The spring force $k x$ which is equal to the tension $F^{^{'}}$ in the string

From the FBD of the pulley we can say that
$F^{^{'}} = 2 F$ ..............(i)
Also, $F^{^{'}} = k x = k . \frac{y}{2}$ .........(ii)
(As displacement in spring due to force $F$ is given as $\frac{y}{2}$ )
So, from (i) & (ii) we have
$\frac{k y}{2} = 2 F ⟹ F = \frac{k y}{4}$

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On applying a force F, point P is displaced vertically down by 'y' from equilibrium position. Find the applied force F in terms of 'y' if the point A is displaced by y2 due to application of F.

On applying a force $F$ , point $P$ is displaced vertically down by 'y' from equilibrium position. Find the applied force $F$ in terms of 'y' if the point $A$ is displaced by $\frac{y}{2}$ due to application of $F$ .