Question

A solid sphere of density $\eta (>1)$ times lighter than water is suspended in a water take by a string tied to its base as shown in the fig. If the mass of the sphere is $m$ theory the tension in the string is given by:

• A. $\left(\frac{\eta -1}{\eta }\right)mg$
• B. $\eta mg$
• C. $\frac{mg}{\eta -1}$
• D. $(\eta -1)mg$

Answer 1

The correct option is A $\left(\frac{\eta -1}{\eta }\right)mg$

The tension in the string is given as,

$T=V\sigma g-V\rho g$

$T=V\eta \rho g-V\rho g$

$T=\left(\eta -1\right)V\rho g$

$T=\left(\eta -1\right)mg$

Thus, the tension in the string is $\left(\eta -1\right)mg$.