Question

A pendulum of mass \( 1 \) kg and length \( l = 1 \) m is released from rest at an angle \( \theta = 60^\circ \). The power delivered by all the forces acting on the bob at angle \( \theta = 30^\circ \) will be (Take, \( g = 10 \) m/s\( ^2 \)):

• A. \( 13.4 \) W
• B. \( 20.4 \) W
• C. \( 24.6 \) W
• D. zero

Hint:

Power is given by \( P = F v \cos \theta \). For pendulum motion, velocity can be found using energy conservation.

Answer 1

The Correct Option is A

Step 1: {Find velocity at \( \theta = 30^\circ \)}
Using energy conservation: \[ v = \sqrt{2 g h} \] Step 2: {Calculate height difference}
\[ h = l (\cos 30^\circ - \cos 60^\circ) \] \[ = 1 \times \left( \frac{\sqrt{3}}{2} - \frac{1}{2} \right) = 0.36 { m} \] Step 3: {Find velocity}
\[ v = \sqrt{2 \times 10 \times 0.36} \] \[ = \sqrt{7.2} = 2.68 { m/s} \] Step 4: {Find power}
\[ P = (mg v) \cos 60^\circ \] \[ = (1 \times 10 \times 2.68) \times \frac{1}{2} \] \[ = 13.4 { W} \] Thus, the correct answer is (A) 13.4 W.