Question

Figure shows a metal ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has height 6 cm, face area $11c{m}^2$ on the top and bottom and density $0.5g/c{m}^3,4cm$ of cylinder's height is inside the water surface. If density of the metal ball is $8gm/c{m}^3$ then its radius is equal to ${\left(\frac{3}{x}\right)}^{1/3}$ cm. calculate x. (${\rho }_w=1gm/c{m}^3$)

• A. $7$
• B. $5$
• C. $3$
• D. $8$

Answer 1

The correct option is D $8$

In the given figure.

$8\times \left(\frac{4}{3}\pi R^3\right)\times g+0.5\left(6\times 11\right)\times g=1\left[\frac{4}{3}\pi R^3+4\times 11\right]g$

$\Rightarrow 7\left[\frac{4}{3}\pi R^3\right]g=11g$

$\Rightarrow R^3=\frac{11\times 3}{28\pi }$

$\Rightarrow R={\left(\frac{11\times 3}{28\pi }\right)}^{1/3}$

$\Rightarrow x=\frac{28\pi }{11}\approx 8$

Hence,

option $\left(D\right)$ is correct answer.