A) \[0.8\text{ }cm\]
B) \[0.4\text{ }cm\]
C) \[0.2\text{ }cm\]
D) \[0.5\text{ }cm\]
Correct Answer: B
Solution :
Radius of vessel (R) = 2 cm Rise in water level \[=0.8\text{ }cm.\] Volume of water displaced by 300 lead balls \[=\pi {{R}^{2}}h=\pi \times 4\times 0.8=3.2\pi \] \[\therefore \]Volume displaced by one ball \[=\frac{\pi \times 3.2}{300}\] \[\therefore \] Let radius of each ball be r cm. \[\therefore \]\[\frac{4}{3}\pi {{r}^{3}}=\frac{\pi \times 3.2}{300}\]\[\Rightarrow \] \[r=\sqrt[3]{\frac{8}{1000}}=\frac{2}{10}=0.2\,cm\] \[\therefore \] Diameter \[2\times r=0.4\,cm\]
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