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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Rotational Mechanics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rotational Mechanics

A simple pendulum of length l is displaced to form an angle heta...

A simple pendulum of length ll is displaced to form an angle hetaheta with the vertical. Calculate the magnitude of the torque exerted by the weight ww of the bob about the point of suspension, and state when this torque is zero.

Options

  1. Awlcos⁡θwl\cos\theta, when the bob is at the lowest point
  2. Bwlsin⁡θwl\sin\theta, when the bob is at an extreme position
  3. Cwlsin⁡θwl\sin\theta, when the bob is at the lowest point
  4. Dwlcos⁡θwl\cos\theta, when the bob is at an extreme position

Correct answer

C. wlsin⁡θwl\sin\theta, when the bob is at the lowest point

Step-by-step solution

The torque about the point of suspension is given by the cross product of the position vector r⃗\vec{r} and the force F⃗\vec{F}.

Here, the force is the weight ww acting vertically downwards, and the magnitude of the position vector is the length of the pendulum ll.

The angle between the position vector and the force vector is θ\theta.

The magnitude of the torque is τ=∣r⃗×F⃗∣=lwsin⁡θ\tau = |\vec{r} \times \vec{F}| = l w \sin\theta.

The torque is zero when τ=0\tau = 0, which implies sin⁡θ=0\sin\theta = 0, giving θ=0\theta = 0.

This condition corresponds to the bob being at its lowest point.
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