Question

A smooth sphere of radius R and M is placed on the smooth horizontal floor. Another 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 –

• A. F = (m + M)g cot q
• B. F = Mg cot q
• C. F = (m + M) g tan q
• D. None of these

Answer 1

Answer: (A)

F = (m + M)g cot q

Answer 2

N sin q = mg and N cos q = ma

\ tan q = $\frac { \mathrm { g } } { \mathrm { a } }$ ̃ a = g cot q

Hence, F = (m + M) g cot q