A small disc is on the top of a smooth hemisphere of radius ' R '. The smallest horizontal velocity ' $V$ ' that should be imparted to the disc so that disc leaves the hemisphere surface without sliding down is (there is no friction)

• A

  $V=\sqrt{g^2 R}$
• B

  $V=\sqrt{2 g R}$
• Correct answer
  C

  $V=\sqrt{g R}$
• D

  $V=\sqrt{g / R}$

Solution

At the top of hemisphere, $\mathrm{mg}-\mathrm{N}=\frac{\mathrm{mv}^2}{\mathrm{R}}$
For the disc leaves the hemisphere, $\mathrm{N}=0 \quad \therefore \mathrm{mg}=\frac{\mathrm{mv}^2}{\mathrm{R}} \Rightarrow \mathrm{v}=\sqrt{\mathrm{gR}}$

Hence, the correct answer is option: 'C'.