Question

The bob of a simple pendulum is given a velocity in horizontal direction when the bob is at lowest position ,so that the bob describes vertical circle of radius equal to length of pendulum and tension in the string is $10N$ when the bob is at an angle ${60}^0$ from lowest position of vertical circle. The tension in the string when the bob reaches highest position is (The mass of bob is $100$ gram. $g=10m{s}^{–2}$):

• A. $9N$
• B. $7N$
• C. $5.5N$
• D. $3.5N$

Answer 1

Answer: (C)

$5.5N$

For a body of mass ${}^{\prime }{m}^{\prime }$ moving in a vertical circle, Tension in the string at highest point and Tension at any angle $\theta$ with vertical is related as:-

$T-T_H=3mg(1+cos\theta )$

Substituting the values

$10-T_H=3\left(0.1\right)\left(10\right)(1+cos{60}^0)=4.5\Rightarrow T_H=5.5N$