Question

Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is 'm', the tension in the string is mg.cosθ
(a) always
(b) never
(c) at the extreme positions
(d) at the mean position.

Answer 1

Answer ⇒ Option (d). At the Extreme Positions.

Reason/Explanation ⇒  As we all know that the Tension in the string is given by mgcosθ only at the extreme positions. To verify this, let us derive the mathematical expression.

Now,

Refers to the attachment for the figure of the Pendulum.

From the Figure, It can be seen that Tension in the string is mgcosθ only at the Extreme positions, whereas on the mean positions it is equal to the mg.

Hence, Correct answer is Option (d).

Hope it helps.

Answer 2

Answer ⇒ Option (d). At the Extreme Positions.