One end of a long iron chain of linear mass density λ is fixed to a sphere of mass m and specific density 13 while the other end is free. The sphere along with the chain is immersed in a deep lake. If specific density of iron is 7, the height above the bed of the lake at which the sphere will float in equilibrium is (Assume that the part of the chain lying on the bottom of the lake exerts negligible force on the upper part of the chain.)

# One end of a long iron chain of linear mass density $\lambda$ is fixed to a sphere of mass m and specific density while the other end is free. The sphere along with the chain is immersed in a deep lake. If specific density of iron is 7, the height above the bed of the lake at which the sphere will float in equilibrium is (Assume that the part of the chain lying on the bottom of the lake exerts negligible force on the upper part of the chain.)

1. A

$\frac{16\mathrm{m}}{7\lambda }$

2. B

$\frac{7\mathrm{m}}{3\lambda }$

3. C

$\frac{5\mathrm{m}}{2\lambda }$

4. D

$\frac{8\mathrm{m}}{3\lambda }$

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### Solution:

For equilibrium, weight = Buoyant force

$⇒\mathrm{h}=\frac{7\mathrm{m}}{3\lambda }$

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