Question

A smooth sphere of radius R and mass M is placed on the smooth horizontal floor. Another smooth particle of mass m is placed on the sphere and a horizontal force F is applied on the sphere as shown. If the particle does not slip on the sphere then the value of force F is ______.

Options

• F = mg cotθ

• F = Mg cotθ

• F = (m + M)g cotθ

• F = (m + M)g tanθ

Answer 1

A smooth sphere of radius R and mass M is placed on the smooth horizontal floor. Another smooth particle of mass m is placed on the sphere and a horizontal force F is applied on the sphere as shown. If the particle does not slip on the sphere then the value of force F is F = (m + M)g cotθ.

Explanation:

By F.B.D of m

N sinθ = mg

and N cosθ = ma

∴ tanθ = `"g"/"a"`

⇒ a = g cotθ

F = (m + M)g cotθ