11.

A ball is hung by a string from the ceiling of a car moving on a straight and smooth road. If the string is inclined towards the front side of the car making a small constant angle with the vertical, then the car is moving with

• constant velocity

• constant acceleration

• constant retardation

• increasing acceleration

A girl in a swing is 2.5 m above ground at the maximum height and at 1.5 m above the ground at the lowest point. Her maximum velocity in the swing is (g = 10 ms^-2)

• $5\sqrt{2} {\mathrm{ms}}^{-1}$

• $2\sqrt{5} {\mathrm{ms}}^{-1}$

• $2\sqrt{3} {\mathrm{ms}}^{-1}$

• $3\sqrt{2} {\mathrm{ms}}^{-1}$

The position of a particle of mass 4 g, acted upon by a constant force is given by x = 4 t², where x is in metre and t in second. The work done during the first 2 s is

• 128 mJ

• 512 mJ

• 576 mJ

• 144 mJ

The shape of the curve representing the relation between the speed and kinetic energy of a moving object is

• parabola

• ellipse

• straight line with positive slope

• straight line with negative slope

A billiard ball of mass m and radius r, when hit in a horizontal direction by a cue at a height h above its centre, acquired a linear velocity v₀. The angular velocity ω₀ acquired by the ball is

• $\frac{5{\mathrm{v}}_0{\mathrm{r}}^2}{2\mathrm{h}}$

• $\frac{2{\mathrm{v}}_0{\mathrm{r}}^2}{5\mathrm{h}}$

• $\frac{2{\mathrm{v}}_0\mathrm{h}}{5{\mathrm{r}}^2}$

• $\frac{5{\mathrm{v}}_0\mathrm{h}}{2{\mathrm{r}}^2}$

A carpet of mass m made of inextensible material is rolled along its length in the form of a cylinder of radius r and kept on a rough floor. The decrease in the potential energy of the system, when the carpet is unrolled to a radius $\frac{\mathrm{r}}{2}$ without sliding is (g = acceleration due to gravity)

• $\frac{3}{4} \mathrm{mgr}$

• $\frac{5}{8} \mathrm{mgr}$

• $\frac{7}{8} \mathrm{mgr}$

• $\frac{1}{2} \mathrm{mgr}$

The radius of gyration of a solid cylinder of mass M and radius R about its own axis is

• $\frac{\mathrm{R}}{\sqrt{2}}$

• $\frac{\mathrm{R}}{2}$

• $\frac{\mathrm{R}}{\sqrt{3}}$

• $\frac{\mathrm{R}}{3}$

An artificial satellite moving in a circular orbit at a distance h from the centre of the earth has a total energy E₀. Its potential energy is

• − E₀

• 1.5 E₀

• E₀

• 2 E₀

Two identical spheres of radius R made of the same material are kept at a distance d apart. Then the gravitational attraction between them is proportional to

• d^-2

• d²

• d⁴

• d

Choose the wrong statement

• The bulk modulus for solids is much larger than for liquids

• Gases are least compressible

• The incompressibility of the solids is due to the tight coupling between neighbouring atoms

• The reciprocal of the bulk modulus is called compressibility