A particle is projected with a velocity v so that its horizontal range twice the greatest height attained. The horizontal range is

• $\frac{4{\mathrm{v}}^2}{5 \mathrm{g}}$

• $\frac{{\mathrm{v}}^2}{\mathrm{g}}$

• $\frac{{\mathrm{v}}^2}{2\mathrm{g}}$

• $\frac{2{\mathrm{v}}^2}{3 \mathrm{g}}$

The velocity-time graph for two bodies A and B are shown in figure. Then, the acceleration of Aand B are in the ratio

• sin 25° to sin 50°

• tan 25° to tan 40°

• cos 25° to cos 50°

• tan 25° to tan 50°

The ratio of the dimensions of Planck's constant and that of moment of inertia has the dimensions of

• angular momentum

• time

• velocity

• frequency

Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is I. Ifthe same rod is bent into a ring and its moment of inertia about its diameter is I', then the ratio $\frac{\mathrm{I}}{\mathrm{I}\text{'}}$ is

• $\frac{2}{3} {\mathrm{\pi }}^2$

• $\frac{3}{2} {\mathrm{\pi }}^2$

• $\frac{5}{3} {\mathrm{\pi }}^2$

• $\frac{8}{3} {\mathrm{\pi }}^2$

If the mass of a body is M on the surface of the Earth, the mass of the same body on the surface of the Moon is

• 6 M

• $\frac{\mathrm{M}}{6}$

• zero

• M

The ratio of angular speed of a second-hand to the hour- hand of a watch is

• $\frac{3600}{1}$

• $\frac{720}{1}$

• $\frac{72}{1}$

• $\frac{60}{1}$

The kinetic energy of a body ofmass 4 kg and momentum 6 N-s will be

• 4.5 J

• 2.5 J

• 5.5 J

• 3.5 J

A stone of mass 0.05 kg is thrown vertically upwards. What is the direction and magnitude of net force on the stone during its upward motion ?

• 0.98 N vertically downwards

• 0.49 N vertically downwards

• 9.8 N vertically downwards

• 0.49 N vertically upwards

The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is

• 2 : 1

• 3 : 1

• 8 : 1

• 4 : 1

1 g of ice is mixed with 1 g of steam. At thermal equilibrium, the temperature of the mixture is

• 50°C

• 0°C

• 55°C

• 100°C