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A sphere of solid material of specific gravity `8` has a concentric spherical cavity and just sinks in water. The ratio of radius of cavity to that of outer radius of the sphere must beA. `7^(1//3)/2`B. `5^(1//3)/2`C. `9^(1//3)/2`D. `3^(1//3)/2` |
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Answer» Correct Answer - A Let `rho` be the density of the material `rho_(0)` be the density of water.When the sphere has just started sinking, the weight of the sphere `=` weight of water displaced (approx). `implies 4/3pi(R^(3)-r^(3))rhog=4/3piR^(3)rho_(0)g` `implies (R^(3)-r^(3))rho=R^(3)rho0implies((R^(3)-r^(3)))/R^(3)=(rho_(0))/(rho)` `rarr r/R=(7^(1/3))/2` |
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