Question

The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is$?$

• A. ${90}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${30}^o$

Answer 1

Answer: (B)

${60}^o$

$T_1-mg=\frac{m{v}^2}{l}$

at other point

$T_2=mgcos\theta$

$4T_1=4T_2$

on solving

$mg+\frac{m{v}^2}{l}=4mgcos\theta$....1

Applying conservation energy

$\frac{m{v}^2}{2}=mgl(1-cos\theta )$.....2

on solving 1 and 2

$cos\theta =\frac{1}{2}\to \theta ={60}^o$