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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

F+Mg+Mak1

b

F+Mg+ak1+k2

c

Mg+ak1+k2

d

F+Mg+ak1+k2k1k2

answer is D.

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Detailed Solution

Free body diagram of lower spring :F+M(g+a)=k1x

The force acting downwards is F+M(g+a) as a is the pseudo acceleration inside the lift. This is k1x.

x=F+Mg+Mak1

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