$A$ uniform rod of mass $M$ and length $L$ is pivoted at one end and is free to rotate in a vertical plane. The rod is released from a horizontal position. When the rod becomes vertical,the reaction force at the pivot is:

$A$ particle is moving in a uniform circular motion with angular momentum $L$. If the frequency of motion is doubled and its kinetic energy is halved,the new angular momentum will be ...

$A$ uniform rod of mass $8m$ and length $6a$ is placed on a horizontal table. Two point masses $m$ and $2m$ are moving with speeds $2v$ and $v$ respectively,as shown in the figure. They strike the rod and stick to it after the collision. Calculate the speed of the centre of mass of the system after the collision.

$A$ thin and uniform rod of mass $M$ and length $L$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement$(s)$ is/are correct,when the rod makes an angle $60^{\circ}$ with vertical? [$g$ is the acceleration due to gravity]
$(1)$ The radial acceleration of the rod's center of mass will be $\frac{3g}{4}$
$(2)$ The angular acceleration of the rod will be $\frac{3\sqrt{3}g}{4L}$
$(3)$ The angular speed of the rod will be $\sqrt{\frac{3g}{2L}}$
$(4)$ The normal reaction force from the floor on the rod will be $\frac{Mg}{16}$

The moment of inertia of a sphere of mass $M$ and radius $R$ is $I$. Which graph represents the variation of $I$ with respect to $R$,keeping $M$ constant?

$A$ uniform bar of length $6l$ and mass $8m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ moving in the same horizontal plane with speed $2v$ and $v$ respectively,strike the bar (as shown in the figure) and stick to the bar after collision. The total rotational kinetic energy about the centre of mass $c$ will be: