A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$, if it just floats on water in a tank is:
A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$, if it just floats on water in a tank is:
- [JEE MAIN 2024]
- A
$\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}$
- B
$\left(\frac{\sigma+1}{\sigma-1}\right)^{\frac{1}{3}}$
- C
$\left(\frac{\sigma-1}{\sigma}\right)^{\frac{1}{3}}$
- D
$\left(\frac{\sigma-2}{\sigma+2}\right)^{\frac{1}{3}}$
Similar Questions
A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3 p$. The complete arrangement is placed in a liquid of density $2 p$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are)
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$(B)$ the net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$
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A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3 p$. The complete arrangement is placed in a liquid of density $2 p$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are)
$(A)$ the net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$
$(B)$ the net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$
$(C)$ the light sphere is partially submerged.
$(D)$ the light sphere is completely submerged.
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