Question

a small ball connected to a light inextensible string can execute SHM with a time period of t=2sec. now the ball is pulled to one side suhc that thread makes theta with the vertical, the ball is pushed with suitable velocity so that it moves on a circulaepath uniformly. if max tension that thread canbear is 4mg fin time period of new motion

Answer 1

1 second

Answer 2

Use $T=2\pi\sqrt{L/g}=2$ to get $L=g/\pi^2$.

For conical pendulum, $T\cos\theta=mg$ and with $T=4mg$ gives $\cos\theta=1/4$.

The period $T' = 2\pi\sqrt{L\cos\theta/g}$ then is

$$T' = 2\pi\sqrt{\frac{g/(π^2)\cdot(1/4)}{g}} = 1\, \text{s}.$$