Question

A pendulum consisting of a small sphere of mass M suspended by an inextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2 Mg, then the maximum angular amplitude of the displacement from the vertical can be :

• A. 0⁰
• B. 30⁰
• C. 60⁰
• D. 90⁰

Answer 1

Answer: (C)

60⁰

Answer 2

T_max = $\frac{mv^{2}}{\mathcal{l}}$+ mg Ž 2mg = $\frac{mv^{2}}{\mathcal{l}}$ + mg

Ž v = $\sqrt{g\mathcal{l}}$ ...(1)

Q $\frac{1}{2}$mv² = mgh \ h = $\frac{v^{2}}{2g}$ = $\frac{\mathcal{l}}{2}$ ...(2)

Q cosq = $\frac{\mathcal{l -}h}{\mathcal{l}}$ = $\frac{1}{2}$

\ q = 60⁰