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 -

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) 0°  (B) 30°  (C) 60°  (D) 90°

Tardigrade Admin · Accepted Answer

∴ Tm a x=(m vA2/l) +mg ∴ 2mg=(m vA2/l)+mg ⇒ vA=√g l ∴ v2=vA2-2gl (1 - cos θ ) ∴ 0=gl-2gl (1 - cos θ ) ⇒ cos θ =1 / 2 ⇒ θ =60°

Q. 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 $2 M g$ , then the maximum angular amplitude of the displacement from the vertical can be -

$0^{\circ}$

$3 0^{\circ}$

$6 0^{\circ}$

$9 0^{\circ}$

$∴ T_{ma x} = \frac{m v _{A}^{2}}{l} + m g$
$∴ 2 m g = \frac{m v _{A}^{2}}{l} + m g \Rightarrow v_{A} = g l$
$∴ v^{2} = v_{A}^{2} - 2 g l (1 - cos θ)$
$∴ 0 = g l - 2 g l (1 - cos θ)$
$\Rightarrow cos θ = 1/2 \Rightarrow θ = 6 0^{\circ}$

Q. 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 2Mg , then the maximum angular amplitude of the displacement from the vertical can be -

0∘

30∘

60∘

90∘