Question

A small block is moving with uniform speed along a circle of radius $R$ with a time period $2.5s$. in horizontal plane on smooth table surface with the help of a light horizontal string. If the radius of circle is reduced by $20\%$. The final time period of same block is:

• A. $1.2s$
• B. $1.6s$
• C. $2.8s$
• D. $3.2s$

Answer 1

The correct option is B $1.6s$

$I_1=m{r}^2$
$w=\frac{4\pi }{5}$
No external torque is applied, so the Angular Momentum is conserved
$I_1{w}_1=I_2{w}_2$

$m{r}^2{w}_1=\frac{16}{25}m{r}^2{w}_2$

$w_2=\frac{25}{16}{w}_1$

$w_2=\frac{5}{4}\pi r/s$

$T_2=1.6sec$