A torque of 1 N-m is applied to a wheel which is at rest. After 2 second the angular momentum in kg-m² /s is

• 0.5

• 1

• 2

• 4

The position vectors of two identical particles with respect to the origin in three-dimensional coordinate system are r₁ and r₂. The position vector of centre of mass of the system is given by

• r₁ + r₂

• 2(r₁ + r₂)

• r₁ − r₂

• $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{2}$

If a body of moment of inertia 2 kg m² revolves about its own axis making 2 rotations per second, then its angular momentum (in Js) is

• $2 \mathrm{\pi }$

• $4 \mathrm{\pi }$

• $6 \mathrm{\pi }$

• $8 \mathrm{\pi }$

A rigid body is the one in which

• it can have only rotational motion

• it can have only translational motion

• the distances between all pairs of particles of the body do not change

• its centre of mass always lies inside the material of the body

Two objects P and Q initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of P is v and that of Q is 2v, the velocity of centre of mass of the system is

• v

• 3v

• zero

• 1.5 v

A body rolls down an inclined plane . If its kinetic energy of rotation is 40% of its kinetic energy of translation motion, then the body is

• hollow cylinder

• ring

• solid disc

• solid sphere

A circular disc A and a ring B have same mass and same radius. If they are rotated with the same angular speed about their own axis, then

• A has less moment of inertia than B

• A has less rotational kinetic energy than B

• A and B have the same angular momentum

• A has greater angular momentum than B

Two discs rotating about their respective axis of rotation with angular speed 2 rad s^-1 and 5 rad s^-1 are brought into contact such that their axes of rotation coincide. Now, the angular speed of the system becomes 4 rads^-1 . If the moment of inertia of the second disc is 1 x 10^-3 kg m² then the moment of inertia of the first disc (in kg m²) is

• 0.25 × 10^-3

• 1.5 × 10^-3

• 0.5 × 10^-3

• 0.75 × 10^-3

A wheel is rotating at 1800 rpm about its own axis. When the power is switched off, it comes to rest in 2 min. Then, the angular retardation in rads^-1 is

• $2\mathrm{\pi }$

• $\mathrm{\pi }$

• $\mathrm{\pi }/2$

• $\mathrm{\pi }/4$

40.

If the angular momentum· of a particle of mass m rotating along a circular path of radius r with uniform speed is L, the centripetal force acting on the particle is

• $\frac{{\mathrm{L}}^2}{{\mathrm{mr}}^3}$

• $\frac{{\mathrm{L}}^2}{\mathrm{mr}}$

• $\frac{\mathrm{L}}{{\mathrm{mr}}^2}$

• $\frac{{\mathrm{L}}^2\mathrm{m}}{\mathrm{r}}$