Question

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

• A. 0⁰
• B. 30⁰
• C. 60⁰
• D. 90⁰

Answer 1

Answer: (C)

60⁰

Answer 2

\ T_max = $\frac{mv_{A}^{2}}{\mathcal{l}}$ + mg

\ 2mg = $\frac{mv_{A}^{2}}{\mathcal{l}}$ + mg ̃ v_A = $\sqrt{g\mathcal{l}}$

\ v² = $v_{A}^{2}$ – 2gl (1 – cos q)

\ 0 = gl – 2gl (1– cos q)

̃ cos q = 1/2 ̃ q = 60⁰