Two balls connected to a light string, as shown in figure. Ball of mass 2 m is given velocity v 0 . Find magnitude of work done (in J) by tension when string becomes tight. Given m = 3 kg , v 0 =

Question

Two balls connected to a light string, as shown in figure. Ball of mass 2 m is given velocity v 0 ​ . Find magnitude of work done (in J) by tension when string becomes tight. Given m = 3 kg , v 0 ​ = 2 m / s .

TestHub · Accepted Answer

When the string becomes taut, momentum is conserved for the two masses.

$2 m v_{0} = (m + 2 m) v \Rightarrow v = \frac{2 v _{0}}{3}$

The magnitude of work done by tension equals the kinetic energy lost.

$∣ W_{T} ∣ = \frac{1}{2} (2 m) v_{0}^{2} - \frac{1}{2} (3 m) (\frac{2 v _{0}}{3})^{2}$

$∣ W_{T} ∣ = \frac{m v _{0}^{2}}{3} = \frac{( 3 ) ( 2 ) ^{2}}{3} = 4 J$

Physics - Center of Mass Question with Solution | TestHub

Doubts & Discussion