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

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

How earth retains most of the atmosphere?

If earth be at one half its present distance from the sun, then how many days will there be in a year?

By which law is the Kepler's law of areas identical?

Do the force of friction and other contact forces arise due to gravitational attraction? If not, then what is the origin of these forces?

Is the Kepler's law kinematic?

Two particular of equal mass m go round a circle of radius R under the action of their mutual gravitational attraction. What is the speed of each particle?

An artificial satellite moving in a circular orbit around the earth has a total energy \({ E }_{ 0 }\) . What is its potential energy?

Two satellites have their masses in the ratio of 3:1. The radii of their circular orbits are in the ratio of 1:4. What is the ratio of total mechanical energy of A and B?

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

A 400 kg satellite is in circular orbit of radius \(2{ R }_{ E }\) about the earth. How much energy is required to transfer it to a circular orbit of radius \(4{ R }_{ E }\) ? What are the change in the kinetic and potential energies?

The world's first artificial satellite launched by USSR was circling the earth at a distance of 896 km. Calculate its orbital speed and period of revolution.

If the earth has a mass nine times and radius twice that of the planet Mars, calculate the maximum velocity by a rocket to pull out of the gravitational force of the Mars.

An artificial satellite is going round the earth, close to the surface. What is the time taken by it to complete one round?

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

Estimate the size of a rockey sphere a density of 3.0g/cm³ from the surface of which you could barely throw a golf ball and have it never back(assume your best throw is 40m/s)

Kabir was feeling very hungry. He had not eaten since morning. He asked his mother for food but she refused saying that solar eclipse is occurring and she would not cook till that got over. Then, kabir went to drink water and saw that water had tulsi leaves in it. He was frustrated as he had studied that solar and lunar eclipse are natural phenomena and has no ill effects on anyone.
When he told this to his mother, she didn't listen to him and asked him not to be orthodox. He went to his friend's house and on the way, he saw that prayers were being done at various place to keep away the ill effects of solar eclipse. Kabir felt embarrassed at the superstitious of people and went to study.
Time period of jupiter is 11.6 years. How far is jupiter from the sun? The distance of the earth from the sun is \(1.5\times 10^{ 11 }m.\)

Consider two solid uniform spherical object of the same density \(\rho \) . One has a radius R and the other a radius 2R. They are in outer space where the gravitational field from other objects are negligible. If they are at rest with their surfaces touching, then what is the contact force between the objects due to their gravitational attraction?

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.