The moment of inertia of a uniform ring of mass m and radius r about an axis, AA' touching the ring tangentially and lying in the plane of the ring only, as shown in figure, is

• $\frac{5}{4} {\mathrm{mr}}^2$

• $\frac{5}{2} {\mathrm{mr}}^2$

• $\frac{1}{4} {\mathrm{mr}}^2$

• $\frac{1}{2} {\mathrm{mr}}^2$

If the disc shown in figure has mass M and it is free to rotate about its symmetrical axis passing through O, its angular acceleration is

• $\frac{6\mathrm{F}}{\mathrm{MR}}$

• $\frac{3\mathrm{F}}{\mathrm{MR}}$

• $\frac{6\mathrm{F}}{5\mathrm{MR}}$

• $\frac{4\mathrm{F}}{\mathrm{MR}}$

A flywheel of moment of inertia 0.4 kg-m² and radius 20 cm is free to rotate about a central axis. If a string is wrapped on its circumference and it is pulled with a force of 10 N, then the change in its angular velocity after 4 s will be

• 10 rad/s

• 20 rad/s

• 40 rad/s

• 5 rad/s

Three identical spheres of mass m each are placed at the corners of an equilateral triangle of side 1 m. Taking one of the corners as the origin, the position vector of centre of mass is

• $\frac{1}{2}\stackrel{\wedge }{\mathrm{i}} + \frac{\sqrt{3}}{2} \stackrel{\wedge }{\mathrm{j}}$

• $\frac{1}{2} \stackrel{\wedge }{\mathrm{i}} + \frac{1}{2\sqrt{3}} \stackrel{\wedge }{\mathrm{j}}$

• $\stackrel{\wedge }{\mathrm{i}} + \stackrel{\wedge }{\mathrm{j}}$

• $2\stackrel{\wedge }{\mathrm{i}} - \stackrel{\wedge }{\mathrm{j}}$

A disc revolves with a speed of $33\frac{1}{3}$ rev min^-1 and a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the disc. If coefficient of friction between the coins and the disc is 0.15, then which of the two coins will revolve with the disc?

• coin placed at a distance 4 cm

• coin placed at a distance 14 cm

• both coins

• Neither one of the coins

A uniform sphere of mass 500 g rolls down a plane surface without slipping on it, so that its centre moves at a speed of 0.02ms^-1 . The total kinetic energy of rolling sphere would be (in J)

• 1.4 × 10^-4 J

• 0.75 × 10^-3 J

• 5.75 × 10^-3 J

• 4.9 × 10^-5 J

If a thin uniform wire of length X having linear mass density D is bent zero into a circular loop (as shown in the figure). What will be the moment of inertia of the loop about axis AB ?

• 3 L²D/ 16 $\mathrm{\pi }$

• 2 L²D/ 3$\mathrm{\pi }$

• 3 L³D/ 8${\mathrm{\pi }}^2$

• 8 L²D/ 13${\mathrm{\pi }}^2$

158.

A solid sphere rolls without slipping and presses a spring of spring constant k as shown in figure. Then, the compression in the spring will be

   

• $\sqrt{\frac{2\mathrm{M}}{3\mathrm{k}}}$

• $\sqrt{\frac{2\mathrm{M}}{5\mathrm{k}}}$

• $\sqrt{\frac{5\mathrm{k}}{7\mathrm{M}}}$

• $\sqrt{\frac{7\mathrm{m}}{5\mathrm{k}}}$

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms^-2, then the maximum angular velocity of the stone will be

• 2 rad s^-1

• 4 rad s^-1

• 8 rad s^-1

• 16 rad s^-1

A force-time graph for a linear motion of a body is shown in the figure. The change in linear momentum between O and 7 s is

• 2 N-s

• 3 N-s

• 4 N-s

• 5 N-s