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

Why does tides arise in the oceans?

Calculate the mass of the sun, given that distance between the sun and the earth is \(1.49\times { 10 }^{ 11 }m\) and \(G=6.67\times { 10 }^{ -11 }Nm^{ 2 }/{ k }g^{ 2 }\).

Why is the atmosphere much rarer on the moon than one earth?

Where does a body weigh more; at the surface of the earth or in a mine?

When a pendulum clock is taken to a mountain, it becomes slow. But a wrist watch controlled by a spring remains unaffected. Explain.

Why a body weighs more at poles and less at equator?

Calculate the force of attraction between two balls, each of mass 1 kg, when their centres are 10 cm apart.

What is the value of gravitational potential at the surface of the earth, referred top zero potential at infinite distance?

The particles of masses 0.2 kg and 0.8 kg are separated by 12cm. At which point from the 0.2 kg particle, the gravitational field intensity due to the particle, the gravitational field intensity due to the two particles is zero?

A mass of 1 g is separated from another mass of 1 g by a distance of 1 cm. How many g-wt of force exists between them?

What is the gravitational potential energy of a body at height h from the earth surface?

Determine the speed of which the earth would have to rotate on its axis so that a person on the equator would weight 3/5 as much as the present.

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?

Define period of revolution.Derive an expression of the period of revolution or time period of satellite.

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface ?

A satellite orbit the earth at a height of 400 km above the surface.How much energy must be expanded to rocket,the satellite out the earth's gravitational influence? Mass of the satellite = 200kg,mass of the earth  = 6.0 x 10²⁴ kg; radius of the earth = 6.4 x 10⁶ m; G = 6.67 x 10^-11 N m² kg^-2.

Calculate the earth's surface potential from the following data.
(i) Radius of the earth, \(R=6.63\times { 10 }^{ 6 }\quad m\)
(ii) Mean density of the earth, \(\rho =5.57\times 10^{ 3 }kgm^{ -3 }\)
(iii) \(G=6.67\times 10^{ -11 }Nm^{ 2 }kg^{ -2 }\)

Calculate the change in the energy of a 500 kg astellite when it falls from an altitude of 200 km to 199km.If this change takes place during one orbit.Calculate the retarding force on the satellite Given,mass of the earth = \(6\times { 10 }^{ 24 }kg\)  and radius of the earth = 6400 km

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is 1.50 × 10⁸ km away from the sun ?

Two stars each of one solar mass (= 2×10³⁰ kg) are approaching each other for a head on collision. When they are a distance 10⁹ km, their speeds are negligible. What is the speed with which they collide ? The radius of each star is 10⁴ km. Assume the stars to remain undistorted until they collide. (Use the known value of G)

Calculate the period of revolution of the Neptune around the sun. Given that radius of its orbit is 30 times the earth's orbital radius around the sun.

A rocket is fired vertically from the surface of the mars with the speed of 2km/s.If 20% of its initial energy is lost due to Martian atmospheric resistance,how far will the rocket go from the surface of the mars before returning it.Mass of the mars = \(6.4\times { 10 }^{ 23 }kg\) radius of the mars = 3395 km,G = \(6.67\times { 10 }^{ -11 }Nm^{ 2 }/{ kg }^{ 2 }\)