Question

Two equal masses each of mass $M$ are joined by a massless rod of length $L$ Now an impulsive $MV$ is given to the mass $M$ making an angle of ${30}^o$ with the length of the rod. The angular velocity of the rod just after imparting the impulse is :

• A. $\frac{v}{L}$
• B. $\frac{2v}{L}$
• C. $\frac{v}{2L}$
• D. $Noneofthese$

Answer 1

The correct option is C $\frac{v}{2L}$

The angle is given as,

$\sin {30}^{\circ }=\frac{r}{L/2}$

$r=\frac{L}{4}$

The angular impulse about the center of mass is given as,

$F=Mv\times r$

$F=Mv\times \frac{L}{4}$

The change in angular momentum is given as,

$I{\omega }_f-I{\omega }_i=Mv\times \frac{L}{4}$

$2\times \frac{M{L}^2\omega }{4}-0=Mv\times \frac{L}{4}$

$\omega =\frac{v}{2L}$

Thus, the angular velocity is $\frac{v}{2L}$.