Question

A stone of mass $100g$ attached to a string of length $50cm$ is whirred in a vertical circle by giving velocity at lowest point as $7m/s$. find the velocity at the highest point.

• A. $6m/s^2$
• B. $5.42m/s^2$
• C. $6.65m/s^2$
• D. $7.42m/s^2$

Answer 1

Answer: (B)

$5.42m/s^2$

Given:$m=100$g$=0.1$kg,$r=50$cm$=0.5$m,$g=9.8$m/$s^2$, $v_L=7$m/s

To find:Velocity at the highest point $v_H$

$v_H=\sqrt{\frac{2\left(T{E}_H\right)}{m}-4gr}$

Calculation:Total energy at highest point,

T.E$\left(H\right)=$K.E at lowest point$=\frac{1}{2}m{v}_L^2$

$\therefore {T.E}_H=\frac{1}{2}\times 0.1\times 7^2$

$=2.45$J

From formula,

$v_H=\sqrt{\frac{2\left(2.45\right)}{0.1}-4\times 9.8\times 0.5}$

$=\sqrt{29.4}=5.422$m/s

The velocity at the highest point is $5.422$m/s