Question

The length of a simple pendulum is $50cm$ and mass of its bob is $0.1kg.$ The bob is given a velocity $5m/s$ along horizontal direction when the bob is at lowest position and the bob describes vertical circle of radius equal to length of pendulum. The position in the vertical circle, where the tension in the string is $4.5N$ is $(g=10m{s}^{-2})$:

• A. highest point
• B. lowest point
• C. at an angle ${60}^0$ from lowest point of vertical circle
• D. at an angle of ${60}^0$ from highest point of vertical circle

Answer 1

The correct option is C at an angle ${60}^0$ from lowest point of vertical circle

Given: $m=0.1kg,T=4.5N$

Let the center of circular motion of bob is at origin, then the tension $T$ at any point on the circle, making an angle $\theta$ with the -ive y-axis is given by:

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

$4.5=3\times 0.1\times 10(1+\cos \theta )$ ,

$⟹$ $4.5=3(1+\cos \theta )$ ,

$⟹$$4.5/3=(1+\cos \theta )$ ,

$⟹$$3/2-1=\cos \theta$ ,

$⟹$$1/2=\cos \theta$ ,

$⟹$$\theta ={60}^o$ ,

Hence, this point will be at an angle of ${60}^o$ from the lowest point of vertical circle.