JEE Main Rotational Motion Practice Questions With Solutions

A thin circular disc of mass $\mathrm{M}$M and radius $\mathrm{R}$R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$\omega. If another disc of same dimensions but of mass $\mathrm{M}/2$M / 2 is placed gently on the first disc co-axially, then the new angular velocity of the system is :

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis $AB$A B as shown in figure is $\sqrt{8/x}$\sqrt{8 / x}. The value of $x$x is :

A particle of mass $\mathrm{m}$m is projected with a velocity '$\mathrm{u}$u' making an angle of ${30}^{\circ }$30^{\circ} with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $\mathrm{h}$h is :

A heavy iron bar of weight $12\mathrm{kg}$12 \textrm{ } kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle ${60}^{\circ }$60^{\circ} with the horizontal, the weight experienced by the man is :

A disc is rolling without slipping on a surface. The radius of the disc is $R$R. At $t=0$t = 0, the top most point on the disc is $\mathrm{A}$A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

Given below are two statements: one is labelled as Assertion $\mathbf{A}$\mathbf{A} and the other is labelled as Reason $\mathbf{R}$\mathbf{R}

Assertion A : An electric fan continues to rotate for some time after the current is switched off.

Reason R : Fan continues to rotate due to inertia of motion.

In the light of above statements, choose the most appropriate answer from the options given below.

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 m/s${}^2$^{2})

The torque of a force $5\hat{i}+3\hat{j}-7\hat{k}$5 \hat{i} + 3 \hat{j} - 7 \hat{k} about the origin is $\tau$\tau. If the force acts on a particle whose position vector is $2i+2j+k$2 i + 2 j + k, then the value of $\tau$\tau will be

A solid cylinder and a solid sphere, having same mass $M$M and radius $R$R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :