Question

A simple pendulum is oscillating with an angular amplitude ${60}^o$. If $m$ is mass of bob and $T_1$, $T_2$ are tensions in the string, when the bob is at extreme position, mean position respectively then is:

A) $T_1=\frac{mg}{2}$
B) $T_2=2mg$
C) $T_1=0$
D) $T_2=3mg$

• A. A and B are true.
• B. A and D are true.
• C. B and C are true.
• D. C and D are true.

Answer 1

The correct option is A A and B are true.

Angular Magnitude is given $\theta ={60}^o$

As we see in figure, At extreme position:

$T_A=mg\cos \theta$

$T_A=mg\cos {60}^o$

$T_A=T_1=\frac{mg}{2}$

As we see in figure, At middle position:

$T_B=mg+F_c$ where $F_c$ is centrifugal force

$T_B=mg+\frac{m{v}^2}{R}$ where $v$ is velocity of pendulum.

Using energy conservation for extreme position and middle position

$v=\sqrt{gR}$

putting values :

$T_B=T_2=mg+\frac{mgR}{R}=2mg$

Hence option A is correct.