The speed of earth's rotation about its axis is o. Its speed is increased to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is

• 1

• 8.5

• 17

• 34

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is

• MR²

• $\frac{1}{2} {\mathrm{MR}}^2$

• $\frac{3}{2} {\mathrm{MR}}^2$

• $\frac{7}{2} {\mathrm{MR}}^2$

Point masses 1,  2,  3  and  4 kg are lying at the points (0, 0, 0),  (2, 0, 0),  (0, 3, 0)  and  (- 2, -2, 0)   respectively. The moment-of inertia of this system about  X-axis  will be

• 43 kg-m²

• 34  kg-m²

• 27  kg-m²

• 72  kg-m²

The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then, its radius of gyration about a parallel axis through its centre of mass will be

• 80 cm

• 8 cm

• 0.8 cm

• 80 m

A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad-s^-2 produced in it due to the torque. Then, moment of inertia of the wheel is (g =10 ms^-2 )

• 2 kg-m²

• 1 kg-m²

• 4 kg-m²

• 8 kg-m²

An object start sliding on a frictionless inclined plane and from same height another object start falling freely.

• both will reach with same speed

• both will reach with same acceleration

• both will reach in same time

• None of the above

Two rigid bodies A and B rotate with rotational kinetic energies E, and E, respectively. The moments of inertia of A and B about the axis of rotation are I_A and I_B respectively.

If ${\mathrm{I}}_{\mathrm{A}} = \frac{{\mathrm{I}}_{\mathrm{B}}}{2}$ and  E_A = 100 = E_B, the ratio of angular momentum (L_A ) of A to the angular  momentum ( L_B ) of B is

• 25

• 5/4

• 5

• 1/4

The working principle of a ball point pen is

• Bernoulli's theorem

• surface tension

• gravity

• viscosity

Progressive waves are represented by the equation y₁ = a sin (ωt - x )  and y₂ = bcos (ωt - x ).  The phase difference wave is

• 0^o

• 45^o

• 90^o

• 180^o

If applied torque on a system is zero, i.e.,Τ = 0 , then for that system

• ω = 0

• α = 0

• J = 0

• F = 0