Question

A simple pendulum is vibrating with an angular amplitude of 90⁰ as shown in the adjoining figure. For what value of a, is the acceleration directed

(i) Vertically upwards?

(ii) Horizontally?

(iii) Vertically downwards?

• A. 0⁰cos^–1$\left( \frac{1}{\sqrt{3}} \right)$, 90⁰
• B. 90⁰, cos^–1$\left( \frac{1}{\sqrt{3}} \right)$, 0⁰
• C. cos^–1$\left( \frac{1}{\sqrt{3}} \right)$, 0⁰, 90⁰
• D. cos^–1$\left( \frac{1}{\sqrt{3}} \right)$, 90⁰, 0⁰

Answer 1

Answer: (A)

0⁰cos^–1$\left( \frac{1}{\sqrt{3}} \right)$, 90⁰

Answer 2

Acceleration is downward at a = 90⁰ and it is upward at a = 0⁰ Acceleration is horizontal where, T cos a = mg

̃ T = $\frac{mg}{\cos\theta}$ ... (1)

\ T = $\frac{mv_{A}^{2}}{r}$ = 2 mg = 3 mg cos a

$\frac{mg}{\cos\alpha} = \frac{m(2gr)}{r}–2mg + 3mg\cos\alpha$

\ cos² a = $\frac{1}{3}$ ̃ a = cos^–1 $\left( \frac{1}{\sqrt{3}} \right)$