System of Particles and Rotational Motion

A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then the relation between the moments of inertia I_X and I_Y is

• I_Y = 321_X

• I_Y = 161_X

• I_Y = I_X

• I_Y = 641_X

The moments of inertia of two freely rotating bodies A and B are I_A and I_B respectively I_A > I_B and their angular momenta are equal. If K_A and K_B are their kinetic energies then

• K_A = K_B

• K_A > K_B

• K_A < K_B

• K_A = 2 K_B

If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of rotation with time period T is

• $\frac{{\mathrm{\pi MR}}^2}{\mathrm{T}}$

• $\frac{{\mathrm{MR}}^2\mathrm{T}}{2\mathrm{\pi }}$

• $\frac{2{\mathrm{\pi MR}}^2}{\mathrm{T}}$

• $\frac{4{\mathrm{\pi MR}}^2}{5\mathrm{T}}$

Angular velocity of second hand of a clock is

• $\frac{\mathrm{\pi }}{30} \mathrm{rad}/\mathrm{s}$

• $\frac{\mathrm{\pi }}{60} \mathrm{rad}/\mathrm{s}$

• $\frac{\mathrm{\pi }}{15} \mathrm{rad}/\mathrm{s}$

• $\frac{\mathrm{\pi }}{2} \mathrm{rad}/\mathrm{s}$

Sphere, disc and ring are allowed to roll down on an inclined plane from its top, then order in which they reach at the bottom will be

• ring, disc, sphere

• sphere, disc, ring

• disc, ring, sphere

• sphere, ring, disc

If we made half the radius of earth, then duration of day will become

• 6 h

• 12 h

• 24 h

• 3 h

The centre of mass of three particles of mass m₁ = 1.0 kg, m₂ = 2.0 kg, and m₃ = 3.0 kg at the corners of an equilateral triangle 1.0 m on a side, as shown in figure

• $\left(\frac{7}{12}\mathrm{m}, \frac{\sqrt{3}}{4}\mathrm{m}\right)$

• $\left(\frac{5}{12}\mathrm{m}, \frac{\sqrt{3}}{5}\mathrm{m}\right)$

• $\left(\frac{5}{13}\mathrm{m}, \frac{\sqrt{3}}{5}\mathrm{m}\right)$

• $\left(\frac{8}{12}\mathrm{m}, \frac{\sqrt{3}}{5}\mathrm{m}\right)$

A system consists of two point masses M and m (< M). The centre of mass of the system is

• at the middle of m and M

• nearer to M

• nearer to m

• at the position of large mass

Two perfectly elastic particles A and B of equal masses travelling along the line joining, them with velocity 15 m/s and 20 m/s respectively collide. Their velocities after the elastic collision will be (in m/s) respectively.

• 0 and 25

• 5 and 20

• 10 and 15

• 20 and 15

If the equation for the displacement of a particle moving on a circular path is given by θ = 2 t³+ 0.5, where θ is in radian and t in second, then the angular velocity of the particle after 2 s from its start is

• 8 rad/s

• 12 rad/s

• 24 rad/s

• 36 rad/s