Question

Two balls of masses $1kg$ each are connected by an inextensible massless string. The system is resting on a smooth horizontal surface. An impulse of $10Ns$ is applied to one of the balls at angle ${30}^o$ with the line joining two balls in horizontal direction as shown in the figure. Assuming that the string remains taut after the impulse, the magnitude of imputes of tension id $\frac{K}{2}\sqrt{3}Ns$. Find the value of $K$.

Answer 1

Along the string both balls have the same velocity

because they are through with string

$\int Tdt$ = 1 v

$\int 10cos30dt-\int Tdt$ = 1 v

$\int 10cos30dt$ - 1 v = 1 v

v = $\frac{1}{2}\int 10cos30dt$

$\int Tdt=\frac{1}{2}\int 10cos30dt$

= $\int 5.\frac{\sqrt{3}}{2}$dt

Impulse of tension = $\frac{\sqrt{3}}{2}$ Ns

so the value of k = 5