$A$ uniform rod of mass $M$ is hinged at its upper end. $A$ particle of mass $m$ moving horizontally strikes the rod at its mid-point elastically. If the particle comes to rest after the collision,find the value of $M/m$.

$A$ thin uniform rod of mass $M$ and length $L$ has its moment of inertia $I_1$ about its perpendicular bisector. The rod is bent in the form of a semicircular arc. Now its moment of inertia through the centre of the semicircular arc and perpendicular to its plane is $I_2$. The ratio of $I_1 : I_2$ will be

Which of the following statements are correct?

$A$ thin uniform rod,pivoted at $O$,is rotating in the horizontal plane with constant angular speed $\omega$,as shown in the figure. At time $t = 0$,a small insect of mass $m$ starts from $O$ and moves with constant speed $v$ with respect to the rod towards the other end. It reaches the end of the rod at time $t = T$ and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $(|\vec{\tau}|)$ on the system about $O$,as a function of time,is best represented by which plot?

$A$ man spinning in free space changes the shape of his body,e.g.,by spreading his arms or curling up. By doing this,he can change his

$A$ body with a moment of inertia of $3 \ kg \cdot m^2$ rotating with an angular speed of $2 \ rad/s$ has the same kinetic energy as a mass of $12 \ kg$ moving with a speed of ......... $m/s$.