11.

A car moves at a speed of 20ms^-1 on a banked track and describes an arc of a circle of radius $40\sqrt{3}$. The angle of banking is (take g = 10 ms^-2)

• 25°

• 60°

• 45°

• 30°

When a body is projected vertically up from the ground with certain velocity, its potential energy and kinetic energy at a point A are in the ratio 2 : 3. If the same body is projected with double the previous velocity, then at the same point A the ratio of its potential energy to kinetic energy is

• 9 : 1

• 2 : 9

• 1 : 9

• 9 : 2

A spring with force constant k is initially stretched by x₁. If it is further stretched by x₂, then the increase in its potential energy is

• $\frac{1}{2}\mathrm{k} ({\mathrm{x}}_2 - {\mathrm{x}}_1{)}^2$

• $\frac{1}{2} \mathrm{k} {\mathrm{x}}_2 ({\mathrm{x}}_2 + 2 {\mathrm{x}}_1)$

• $\frac{1}{2} \mathrm{k} {{\mathrm{x}}_1}^2 + \frac{1}{2} \mathrm{k} {{\mathrm{x}}_2}^2$

• $\frac{1}{2} \mathrm{k} ({\mathrm{x}}_1 + {\mathrm{x}}_2{)}^2$

A force F_x acts on a particle such that its position x changes as shown in the figure.

The work done by the particle as it moves from x = 0 to 20 m is

• 37.5 J

• 10 J

• 45 J

• 22.5 J

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

Angular momentum of the Earth revolving around the Sun in a circular orbit of radius R is proportional to

• $\sqrt{\mathrm{R}}$

• R

• R²

• R^1/3

A body of mass m is released from a height equal to the radius R of the Earth. The velocity with which it will strike the Earth's surface is

• $\sqrt{2\mathrm{gR}}$

• $\sqrt{\mathrm{gR}}$

• $\sqrt{2 \mathrm{mgR}}$

• $\sqrt{\mathrm{mgR}}$

A satellite revolves around the Earth of radius R in a circular orbit of radius 3R. The percentage increase in energy required to lift it to an orbit of radius 5R is

• 10 %

• 20 %

• 30 %

• 40 %