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Q.

When force F is applied to the combination of two springs (shown in figure), the elongation in upper spring will be (the whole system is inside a lift moving upwards with a constant acceleration a). The upper spring is ideal while the lower spring has mass M. Assume that the deformation of the springs are constant

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a

$\frac{F + M g + M a}{k_{1}}$

b

$\frac{(F + M (g + a))}{k_{1} + k_{2}}$

c

$\frac{M (g + a)}{k_{1} + k_{2}}$

d

$\frac{[F + M (g + a)] (k_{1} + k_{2})}{k_{1} k_{2}}$

answer is D.

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Detailed Solution

Free body diagram of lower spring $: F + M (g + a) = k_{1} x$

The force acting downwards is $F + M (g + a)$ as a is the pseudo acceleration inside the lift. This is $k_{1} x .$

$\Rightarrow x = \frac{F + M g + M a}{k_{1}}$

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When force F is applied to the combination of two springs (shown in figure), the elongation in upper spring will be (the whole system is inside a lift moving upwards with a constant acceleration a). The upper spring is ideal while the lower spring has mass M. Assume that the deformation of the springs are constant