A satellite is orbiting the earth. If its distance from the earth is increased, its

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth,is

If three uniform spheres, each having mass M and radius r, are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

If a particle is fired vertically upwards from the surface of earth and reaches a height of 6400 km, the initial velocity of the particle is (assume R = 6400 km and g = 10 ms^-2)

If M is the mass of the earth and R its radius, the ratio of the gravitational acceleration and the gravitational constant is

A satellite is launched into a circular orbit of radius R around the earth. A second satellite launched into an orbit of radius 1.01 R. The time period of the second satellite is larger than that of the first one by approximately

A plant moving along an elliptical orbit is closet to the Sun at a distance r₁ and farthest away at a distance of r₂ . If V₁ and V₂ are the linear velocities at these points respectively, then find the ratio v_1/v₂

The orbiting velocity of an earth-satellite is 8 kms^-1 .What will be the escape velocity?

A satellite does not need any fuel to circle around the earth.Why?

Two artificial satellites, one of mass 400 kg and another of mass 2500 kg, are set in the same orbit around a planet. What is the ratio of their (i) orbital velocities, (ii) time periods?

The distances of two planets from the sun are 10¹³ m and 10¹² m, respectively. Calculate the ratio of time period and the speeds of the two planets

If the earth is 1/4 of its present distance from the sun, then what is the duration of he year?

Does the escape speed of a body from the earth depends on the location from where it is projected

Does the escape speed of a body from the earth depends on the direction of the projection

What is the height at which the value of g is the same as at a depth of \(\frac{R}{2}?\)

An earth's satellite has a period of 90 min.Assuming the orbit to be circular, calculate its height.Take radius of the earth equal to 6380 km and g at the surface of the earth equal 9.8m/s² .

Choose the correct alternatives.
Acceleration due to gravity increases/decreases with increasing depth(assume the earth to be a sphere of uniform density).

Two satellites S₁ and S₂ revolve round a planet in coplanar circular orbit in the same sense. Their periods of revolution are one hour and 8 hours respectively. The radius of the orbit of S₁ is 10⁴ km. When S₂ is close to S₁ find
(i) the speed of S₂ relative to S₁
(ii) the angular speed of S₂ as actually observed by an astronaut in S₁.