$A$ particle of mass $m$ is projected with a velocity $u$ making an angle $45^o$ with the horizontal. The magnitude of the torque due to weight of the projectile, when the particle is at its maximum height, about the point of projectile
$mu^2$
$\frac{3}{4}\,mu^2$
$\frac{1}{4} \,mu^2$
$\frac{1}{2}\, mu^2$
A $T-$ shaped object of uniform thickness and same material with dimensions shown in the figure, is lying on a smooth floor. A force $\vec F$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translation motion without rotation. Find the location of $P$ with respect to $C$
A solid cylinder rolls without slipping down an inclined plane of height $h$. The velocity of the cylinder when it reaches the bottom is
A rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time, when the rod makes an angle $\theta$ with horizontal the velocity of $COM$ of the rod is $v_0$ . The velocity of the end of the rod in contact with the surface at that instant is
If a solid sphere is rolling, the ratio of its rotational energy to the total kinetic energy is given by
A balloon of mass $M$ with a light rope and monkey of mass $m$ are at rest in mid air. If the monkey climbs up the rope and reaches the top of the rope, the distance by which the balloon descends will be(Total length of the rope is $L$ )