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
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
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
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
A.
Given, F1 = F2 = F and θ = 60°
Resultant force =
∴ Force on mass at A due to mass at B and C
Centripetal force for circumscribing the triangle in a circular orbit is provided by mutual gravitational interaction.
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
E
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