A particle is kept at rest at the top of a sphere of diameter 42 m . When disturbed slightly, it slides down. At what height $h$ from the bottom, the particle will leave the sphere?

• A

  14 m
• B

  28 m
• Correct answer
  C

  35 m
• D

  7 m

Solution

The condition of slipping by particle from top is given by $\cos \theta=2 / 3$ From the figure, $h=r \cos \theta=21 \times \frac{2}{3}=14 \mathrm{~m}$ Therefore, the required height at which the particle will leave the sphere is $=21+h=21+14=35 \mathrm{~m}$

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