Question

Determine the loss in kinetic energy of the system as whole as a result of the collision.

• A. $\frac{1}{6}m{v}^2$
• B. $\frac{1}{7}m{v}^2$
• C. ${mv}^2$
• D. $\frac{{mv}^2}{5}$

Answer 1

The correct option is A $\frac{1}{6}m{v}^2$

Initial K.E, $E_i=\frac{1}{2}m{v}^2+0$

$E_i=\frac{1}{2}m{v}^2$

Final K.E, $E_f=\frac{1}{2}\left(3m\right)(v^{\prime }{)}^2+\frac{1}{2}{I}_{CM}{w}^2$

Putting the values, $E_f=\frac{1}{2}\left(3m\right)(\frac{v}{3}{)}^2+\frac{1}{2}\times \frac{m{l}^2}{3}\times \frac{v^2}{l^2}$

$⟹E_f=\frac{1}{3}m{v}^2$

Loss in K.E, $\Delta E=E_i-E_f=\frac{1}{2}m{v}^2-\frac{1}{3}m{v}^2$

$\Delta E=\frac{1}{6}m{v}^2$