The angular momentum of a rotating body changes from A_o to 4A_o in 4 minutes. The torque acting on the body is:

• 3/4 A_o

• 4A_o

• 3A_o

• 3/2A_o

If a spherical ball rolls on a table without slipping the friction of its total energy associated with rotational energy is :

• 3/5

• 2/7

• 2/5

• 3/7

The equation of stationary wave along a stretched string is given by $\mathrm{y} = 5 \sin \frac{\mathrm{\pi x}}{3} \cos 40\mathrm{\pi t}$ where, x and y are in cm and t in second. The separation between two adjacent nodes is :

• 1.5 cm

• 3 cm

• 6 cm

• 4 cm

54.

If the angle between the vectors $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}} \mathrm{is} \mathrm{\theta }$, the value of the product $\left(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{A}}\right). \overrightarrow{\mathrm{A}}$ is equal to

• ${\mathrm{BA}}^2 \mathrm{cos\theta }$

• BA² sinθ

• BA² sinθ cosθ

• zero

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

• $\frac{1}{2} {\mathrm{MR}}^2$

• MR²

• $\frac{7}{2} {\mathrm{MR}}^2$

• $\frac{3}{2} {\mathrm{MR}}^2$

A force of $-\mathrm{F} \hat{\mathrm{k}}$ acts on O, the origin of the coordinate systems. The torque about the point (1, -1 ) is

• $\mathrm{F} \left(\hat{\mathrm{i}} - \hat{\mathrm{j}}\right)$

• $- \mathrm{F} \left(\hat{\mathrm{i}} + \hat{\mathrm{j}}\right)$

• $\mathrm{F} \left(\hat{\mathrm{i}} + \hat{\mathrm{j}} \right)$

• $-\mathrm{F} \left(\hat{\mathrm{i}} - \hat{\mathrm{j}}\right)$

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