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Question

A block of mass m placed on a smooth floor is connected to a fixed support with the help of a spring of stiffness k. It is pulled by a rope as shown in the figure. Tension force T of the rope is increased gradually without changing its direction until the block losses contact from the floor. The increase in rope tension T is so gradual that acceleration in the block can be neglected. What is the extension in the spring, when the block losses contact from the floor?

A
mg cos θk
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B
mg sin θk
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C
mg tan θk
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D
mg cot θk
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Solution

The correct option is D mg cot θk
Free body diagram of the block, before it loses contact with the floor.

When the block is about to leave the floor, it is not pressing the floor.
Therefore N=0 and the block is in equilibrium.
Fx=0T cos θ=kx(i)
Fy=0T sin θ=mg (as N = 0)(ii)
From equation (i) and (ii), we have x=mgcotθk

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