Properties Of Matter Ques 53
- A solid sphere of radius $R$ and density $\rho$ is attached to one end of a massless spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3 \rho$. The complete arrangement is placed in a liquid of density $2 \rho$ and is allowed to reach equilibrium. The correct statement(s) is (are)
(2013 Adv.)
(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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Answer:
Correct Answer: 53.(a,d)
Solution:
Formula:
On small sphere
$ \frac{4}{3} \pi R^{3}(\rho) g+k x=\frac{4}{3} \pi R^{3}(2 \rho) g $ $\quad$ …….(i)
On second sphere (large)
$ \frac{4}{3} \pi R^{3}(3 \rho) g=\frac{4}{3} \pi R^{3}(2 \rho) g+k x $ $\quad$ …….(ii)
By Eqs. (i) and (ii), we get
$ x=\frac{4 \pi R^{3} \rho g}{3 k} $
BETA
