A satellite revolves around the Earth of radius R in a circular orbit of radius 3R. The percentage increase in energy required to lift it to an orbit of radius 5R is

• 10 %

• 20 %

• 30 %

• 40 %

Pick out the wrong statement from the following

• The SI unit of universal gravitational constant is Nm²kg^-2

• The gravitational force is a conservative force

• $\mathrm{Gravitational} \mathrm{potential} \mathrm{energy} = \frac{\mathrm{gravitational} \mathrm{potential}}{\mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{body}}$

• The centripetal acceleration of the satellite is equal to acceleration due to gravity

If a body of mass m has to be taken from the surface to the earth to a height h = R, then the amount of energy required is (R = radius of the earth)

• mgR

• $\frac{\mathrm{mgR}}{3}$

• $\frac{\mathrm{mgR}}{2}$

• $\frac{\mathrm{mgR}}{12}$

The total energy of an artificial satellite of mass m revolving in a circular orbit around the earth with a speed v is

• $\frac{1}{2} {\mathrm{mv}}^2$

• $\frac{1}{4} {\mathrm{mv}}^2$

• $- \frac{1}{2} {\mathrm{mv}}^2$

• − mv²

The total energy and kinetic energy of an Earth's satellite are respectively

• positive and negative

• negative and positive

• positive and positive

• negative and negative

If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to

• half of the present year

• $\frac{1}{4}\mathrm{th}$ of the present year

• $\frac{1}{8}\mathrm{th}$ of the present year 

• $\frac{7}{8}\mathrm{th}$ of the present year

The angle of dip at a place where horizontal and vertical components of Earth's magnetic field are equal is

• 45°

• 30°

• 0°

• 60°

An astronaut experiences weightlessness in a space satellite. It is because

• the gravitational force is small at that location in space

• the gravitational force is large at that location in space

• the astronaut experiences no gravity

• the gravitational force is infinitely large at that location in space

An artificial satellite moving in a circular orbit at a distance h from the centre of the earth has a total energy E₀. Its potential energy is

• − E₀

• 1.5 E₀

• E₀

• 2 E₀

Two identical spheres of radius R made of the same material are kept at a distance d apart. Then the gravitational attraction between them is proportional to

• d^-2

• d²

• d⁴

• d