The height of the dam, in a hydroelectric power station is 10 m. In order to generate 1 MW of electric power, the mass of water (in kg) that must fall per second on the blades of the turbines is

• 10⁶

• 10⁵

• 10³

• 10⁴

A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, the velocity of the ball is

• 50 ms^-1

• 9 ms^-1

• 90 ms^-1

• 60 ms^-1

A particle is moving under the influence of a force given by F = kx, where k is a constant and x is the distance moved. The energy (in joules) gained by the particle in moving from x = 0 to x = 3 is

• 2 k

• 3.5 k

• 4.5 k

• 9 k

14.

A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity ω. Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

• 4ω

• $\frac{\mathrm{M}}{4\mathrm{m}} \mathrm{\omega }$

• $\left(\frac{\mathrm{M}}{\mathrm{M} + 4\mathrm{m}}\right) \mathrm{\omega }$

• $\left(\frac{\mathrm{M}}{\mathrm{M} - 4\mathrm{m}}\right) \mathrm{\omega }$

The angular velocity of a wheel increases from 100 rps to 300 rps in 10 s. The number of revolutions made during that time is

• 600

• 1500

• 2000

• 3000

Three identical spheres, each of mass 3 kg are placed touching each other with their centres lying on a straight line. The centres of the sphere are marked at P, Q and R respectively. The distance of centre of mass of system from P is

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

• $\frac{\mathrm{PQ} + \mathrm{PR}}{3}$

• $\frac{\mathrm{PQ} + \mathrm{QR} + \mathrm{PR}}{9}$

• $\frac{\mathrm{PQ} + \mathrm{PR}}{9}$

Infinite number of masses, each 1 kg, are placed along the x-axis at x = ± 1m, ± 2 m, ± 4 m, ± 8 m, ±16m. The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin (x = 0) is

• G/2

• G

• 2G

• 4G

Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is

• $\sqrt{\frac{\mathrm{GM}}{\mathrm{L}}}$

• $\sqrt{\frac{3\mathrm{GM}}{2\mathrm{L}}}$

• $\sqrt{\frac{3\mathrm{GM}}{\mathrm{L}}}$

• $\sqrt{\frac{2\mathrm{GM}}{3\mathrm{L}}}$

A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is

• 2E

• $\sqrt{\mathrm{E}}$

• E

• $\sqrt{\mathrm{E}}/2$

Eight drops of a liquid of density ρ and each of radius a are falling through air with a constant velocity 3. 75 cms^-1. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

• 1.5 × 10^-2 ms^-1

• 2.4 × 10^-2 ms^-1

• 15 × 10^-2 ms^-1

• 25 × 10^-2 ms^-1