Two masses are attached to a rod end to end. If torque is applied they rotate with angular acceleration $\mathrm{\alpha }$. If their distances are doubled  and same torque is applied, then they move with angular acceleration

• 4 α

• α

• 3 α

• α/4

A body of mass M moving with velocity V explodes into two equal parts. Id one comes to rest and the other moves with velocity v, what would be the value of v?

• V

• $\frac{\mathrm{V}}{\sqrt{2}}$

• 4V

• 2V

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

• $\frac{\mathrm{M} {\mathrm{R}}^2 \mathrm{T}}{2\mathrm{\pi }}$

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

• $\frac{\mathrm{\pi } \mathrm{M} {\mathrm{R}}^3}{\mathrm{T}}$

• $\frac{2\mathrm{\pi } \mathrm{M} {\mathrm{R}}^2}{\mathrm{T}}$

A spherical solid ball of mass 1 kg and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 rad/s. The kinetic energy of rotation is

• 4500J

• 90J

• 910J

• 0.45J

4. The moment of inertia of a thin spherical shell of mass M and radius R about a diameter is$\frac{2}{3}{\mathrm{MR}}^2$. Its radius of gyration K about a tangent will be

• $\sqrt{\frac{2}{3}}\mathrm{R}$

• $\frac{2}{3}\mathrm{R}$

• $\frac{5}{3}\mathrm{R}$

• $\sqrt{\frac{5}{3}}\mathrm{R}$

The moment of inertia of a body about a given axis is 1.2 kg-m². Initially, the body is at rest. In order to produce rotational kinetic energy of 1500 J, angular acceleration of 25 rad/s² must be applied about the axis for a duration of

• 4s

• 2s

• 8s

• 10s

Three particles, each of mass m gram are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm² units will be

• $\frac{3}{4}{\mathrm{ml}}^2$

• 2 ml²

• $\frac{5}{4}{\mathrm{ml}}^2$

• $\frac{3}{2}{\mathrm{ml}}^2$

Two discs of the moment of inertia I₁ and l₂ and angular speeds ω₁ and ω₂, are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate combinedly along the same axis the rotational KE of the system will be

• $\frac{{\mathrm{I}}_1{\mathrm{\omega }}_1 + {\mathrm{I}}_2{\mathrm{\omega }}_2}{2({\mathrm{I}}_1 + {\mathrm{I}}_2)}$

• $\frac{({\mathrm{I}}_1 + {\mathrm{I}}_2)({\mathrm{\omega }}_1 +{\mathrm{\omega }}_2{)}^2}{2}$

• $\frac{({\mathrm{I}}_1{\mathrm{\omega }}_1 + {\mathrm{I}}_2{\mathrm{\omega }}_2{)}^2}{2({\mathrm{I}}_1+ {\mathrm{I}}_2)}$

• None of these

Which of the following has centre of mass not situated in the material of the body?

• A rod bent in the form of a circle

• Solid sphere

• Cricket bat

• None of the above

A rod of length L, whose lower end is sliding along the horizontal plane, starts to topple from the vertical position. The velocity of the upper end when it hits the ground is

• $\sqrt{\mathrm{gL}}$

• $\sqrt{3\mathrm{gL}}$

• $\sqrt{5\mathrm{gL}}$

• $3\sqrt{\mathrm{gL}}$