Question

Two balls of masses $1kg$ each are connected by an inextensible massless spring. The system is resting on a smooth horizontal surface. An impulse of $10N$s is applied to one of the balls at an 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 impulse of tensions is:

• A. $6Ns$
• B. $\frac{5}{2}\sqrt{3}Ns$
• C. $5Ns$
• D. $\frac{5}{\sqrt{3}}Ns$

Answer 1

Answer: (B)

$\frac{5}{2}\sqrt{3}Ns$

Refer image,

We know that,

Impulse = Change in momentum

$10NS=mv$

$V=10m/s$

To find out impulse of tension, we have to look for change in momentum along the string.

Along the string on both mass

Impulse = $2J_s$ = Change in momentum

$=mv\cos {30}^0$

$J_S=\frac{m}{2}v\cos {30}^0$

$J_S=\frac{5\sqrt{3}}{2}$