Target Physics [XI DPP 40] ROTATION (Rotational Kinetics)

A ring or radius 3a is fixed rigidly on a table. A small ring whose mass is m and radius a, rolls without slipping inside it as shown in the figure. The small ring is released from position A. When it reaches at the lowest point, the speed of the centre of the ring at that time would be -

• $\sqrt{2ga}$

• $\sqrt{3ga}$

• $\sqrt{6ga}$

• $\sqrt{4ga}$

A thin rod is hinged at one end O and it is in an unstable equilibrium position. It falls under gravity due to a slight disturbance. It makes angles 60º, 90º and 180º with vertical in positions (B), (C) and (D) respectively. If  $ω_2,ω_3,ω_4$   are angular velocities at these positions, then - 

•  $ω_4=2ω_3$  

•  $ω_4=2ω_2$  

•  $ω_4=1.5ω_2$  

•  $ω_4=\sqrt{2}ω_2$  

A disc of mass M and radius R is suspended in a vertical plane by a horizontal axis passing through its centre. After sticking an object of same mass M at its rim the mass is raised to the position of maximum height. Now this unstable system is released. When the object passes the position right below the centre the angular velocity of the system would be -

• $\sqrt{\frac{8g}{3R}}$

• $\sqrt{\frac{2g}{3R}}$

• $\sqrt{\frac{3g}{2R}}$

• $\sqrt{\frac{3g}{8R}}$

A solid cylinder of mass 250gm and radius 4cm is rolling down an inclined plane. The angle of inclination of the plane with horizontal is $\theta=\sin^{-1}\ \left(\frac{1}{10}\right).$ Total kinetic energy of the cylinder after 5 seconds would be-

• 0.02 joule

• 0.2 joule

•  2.0 joules

• 20 joules 

A solid iron sphere A rolls down an inclined plane, while another hollow sphere B with the same mass and external radius also rolls down the inclined plane. If V_A and V_B are their velocities at the bottom of the inclined plane, then

• V_A > V_B

• V_A = V_B

• V_A < V_B

• V_A > = < V_B

A solid iron sphere A rolls down an inclined plane, while another hollow sphere B with the same mass and external radius also rolls down the inclined plane. If V_A and V_B are their velocities at the bottom of the inclined plane, then

In above question if E_A and E_B be the total kinetic energies of A and B, then

• E_A > E_B

• E_A = E_B

• E_A < E_B

• E_A > = < E_B

Two bodies with moments of inertia I₁ and I₂ ( I₁ > I₂) have equal angular momenta. If kinetic energy of rotation are E₁ and E₂

• E₁ = E₂

• E₁ > E₂

• E₁ < E₂

• E₁ > = < E₂

A rigid body of mass m rotates with angular velocity ω about an axis at a distance a from the centre of mass G. The radius of gyration about a parallel axis through G is k. The kinetic energy of rotation of the body is

• $\frac{1}{2}mk^2\omega^2$

• $\frac{1}{2}ma^2\omega^2$

• $\frac{1}{2}m\left(a^2+k^2\right)\omega^2$

• $\frac{1}{2}m\left(a+k\right)^2\omega^2$

A metal sphere of radius R and specific heat s is rotating at a speed of n rotations per second about its central axis. It is suddenly stopped and 50% of its energy is converted into heat, the rise in temperature will be -

• $\frac{2}{5}\ JR^2\pi^2n^2s$

• $\frac{4}{5}\ \frac{R^2\pi^2n^2}{Js}$

• $\frac{4}{5}\ \frac{J^2R^2\pi^2n^2}{s}$

• $\frac{2}{5}\ \frac{R^2\pi^2n^2}{Js}$

Two identical discs roll from rest on two inclined planes of length S and 2S as shown. The velocities v₁ and v₂ acquired by the discs at the bottom are related as -

• v₁ = v₂/4

• v₁ = v₂/2

• v₁ = v₂

• v₁ = 2v₂