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Q.

A cubical wooden block of side L and relative density 0.5 is floating on the surface of water as shown in the figure. A string is attached to it through an ideal pulley fixed to the bottom of vessel as shown in figure. The graph of tension T in the string vs distance of the bottom of the block from the free surface of the water when the end A of the rope is slowly pulled up will be (block is moving very slowly and the vessel is very wider):

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a

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b

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c

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d

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answer is B.

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Detailed Solution

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Let y is the additional length immersed. Distance of bottom face of cube from free
surface of liquid is $z = L 2 + y ⇒ y = z − L 2$
Again, tension = extra force of buoyancy developed
$T = y L 2 ρ g = z − L 2 L 2 ρ g$
$T = (L^{2} ρ g) z - \frac{L^{3}}{2} ρ g$
$T = k_{1} z - k_{2} u p t o z = L$
After z = L, buoyancy will not change and hence T does not change as the body is completely immersed.

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A cubical wooden block of side L and relative density 0.5 is floating on the surface of water as shown in the figure. A string is attached to it through an ideal pulley fixed to the bottom of vessel as shown in figure. The graph of tension T in the string vs distance of the bottom of the block from the free surface of the water when the end A of the rope is slowly pulled up will be (block is moving very slowly and the vessel is very wider):