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

123.

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

• $\sqrt{\mathrm{gL}}$

• $\sqrt{3\mathrm{gL}}$

• $\sqrt{5\mathrm{gL}}$

• $3\sqrt{\mathrm{gL}}$

Two bodies of moments of inertia I₁ and I₂ (I₁ > I₂) have equal angular momentum. If E₁ and E₂ are their kinetic energies of rotation, then

• E₁ > E₂

• E₁ = E₂

• E₁ < E₂

• Cannot be said

A coin placed on a rotating turntable just slips if it is placed at a distance of 8 cm from the centre. If angular velocity of the turntable is doubled, it will just slip at a distance of :

• 1 cm

• 2 cm

• 4 cm

• 8 cm

A solid sphere is rotating about a diameter at an angular velocity ω. If it cools so that its radius reduces to $\frac{1}{\mathrm{n}}$ of its original value, its angular velocity becomes:

• $\frac{\mathrm{\omega }}{\mathrm{n}}$

• $\frac{\mathrm{\omega }}{{\mathrm{n}}^2}$

• nω

• ${\mathrm{n}}^2\mathrm{\omega }$

Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

• 1 kg m²

• 0.1 kg m²

• 2 kg m²

• 0.2 kg m²