Q44 / 60 · KVPY 2012 (SA) · Physics

A solid cube and a solid sphere both made of same material are completely submerged in water but to different depths. The sphere and the cube have same surface area. The buoyant force is-

A
Greater for the cube than the sphere
Correct answer
B
Greater for the sphere than the cube
C
Same for the sphere and the cube
D
Greater for the object that is submerged deeper

Solution

buyount force $\mathrm{B}=\mathrm{V} \rho_{l} \mathrm{~g}, \frac{\mathrm{V}_{\text {cube }}}{\mathrm{V}_{\text {spbere }}}=\frac{\mathrm{a}^{3}}{\frac{4}{3} \pi \mathrm{R}^{3}}$ but it is given $6 \mathrm{a}^{2}=4 \pi \mathrm{R}^{2}$ so, $\frac{\mathrm{V}_{\text {cube }}}{\mathrm{V}_{\text {spbere }}}=\frac{\sqrt{\pi}}{\sqrt{6}}$

Hence, the correct answer is option: 'B'.

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