A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 1 kgm² and its rate of rotation 2 rev/s. The angular momentum is

• 1.257 kg m²/s

• 12.57 kg m²/s

• 13.57 kg m²/s

• 20 kg m²/s

A particle of mass m = 5 units is moving with a uniform speed v = $3\sqrt{2}$ m in the XOY plane along the line Y = X + 4. The magnitude of the angular momentum about origin is

• zero

• 60 unit

• 7.5 unit

• $40\sqrt{2} \mathrm{unit}$

If the length of the second's hand in a stop-clock is 3 cm, the angular velocity and linear velocity of the tip is

• 0.2047 rad/s, 0.0314 ms^-1

• 0.2547 rad/s, 0.314 ms^-1

• 0.1472 rad/s, 0.06314 ms^-1

• 0.1047 rad/s, 0.00314 ms^-1

Three identical spheres, each of mass 1 kg are kept as shown in figure below, touching each other, with their centres on a straight line. If their centres are marked P,Q, R respectively, the distance of centre of mass of the system from P is

• $\frac{\mathrm{PQ}\hspace{0.17em}+ \mathrm{PR}\hspace{0.17em}+ \mathrm{QR}}{3}$

• $\frac{\mathrm{PQ}\hspace{0.17em}+ \mathrm{PR}}{3}$

• $\frac{\mathrm{PQ}\hspace{0.17em}+ \mathrm{QR}}{3}$

• $\frac{\mathrm{PR}\hspace{0.17em}+ \mathrm{QR}}{3}$

The moment of inertia of a thin rod of mass M and length L, about an axis perpendicular to the rod at a distance $\frac{\mathrm{L}}{4}$ from one end is

• $\frac{{\mathrm{ML}}^2}{6}$

• $\frac{{\mathrm{ML}}^2}{12}$

• $\frac{7{\mathrm{ML}}^2}{48}$

• $\frac{7{\mathrm{ML}}^2}{12}$

Moment of a couple is called

• impulse

• couple

• torque

• angular momentum

An athlete throws a discus from rest to a final angular velocity of 15 rad/s in 0.270 s before releasing it. During acceleration, discus moves a circular arc of radius 0.810 m. Acceleration of discus before it is released is

• 45 ms^-2

• 182 ms^-2

• 187 ms^-2

• 192 ms^-2

A motor is rotating at a constant angular velocity of 600 rpm. The angular displacement per second is

• $\frac{3}{50 \mathrm{\pi }} \mathrm{rad}$

• $\frac{3\mathrm{\pi }}{50} \mathrm{rad}$

• $\frac{50 \mathrm{\pi }}{3} \mathrm{rad}$

• $\frac{3\mathrm{\pi }}{25} \mathrm{rad}$

Total angular momentum of a rotating body remains constant, if the net torque acting on the body is

• zero

• maximum

• minimum

• unity

When a ceiling fan is switched on it makes 10 rotations in the first 3s. The number of rotations it makes in the next 3 s, assuming uniform angular acceleration is

• 40

• 30

• 20

• 10