Question

A small block is placed at the top of a sphere. It slides on the smooth surface of the sphere. The angle made by the radius vector of the block with the horizontal when the block leaves the sphere is

• A. 24⁰
• B. 36⁰
• C. 42⁰
• D. 15⁰

Answer 1

Answer: (C)

42⁰

Answer 2

Using $\frac{mv^{2}}{R}$ = mg sin θ

where v = $\sqrt{2gh}$

and sin θ = $\frac{R - h}{R},$ we get

$\frac{m \times 2gh}{R} = mg\sin\theta = mg\frac{R - h}{R}$

or h = R/3 and sin θ = 2/3

or θ = 42⁰