If $r_p, v_p, L_p$ and $r_a, v_a, L_a$ are radii, velocities and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively, then

The total energy of a satellite in a circular orbit at a distance $(R+h)$ from the centre of the Earth varies as [ $R$ is the radius of the Earth and $h$ is the height of the oribit from Earth's surface]

What is the value of acceleration due to gravity at a height equal to half the radius of the Earth, from its surface ?

When a planet revolves around the Sun, in general, for the planet

Electrical as well as gravitational affects can be thought to be caused by fields. Which of the following is true for an electrical or gravitational field?

Two bodies of masses $$8 \mathrm{~kg}$$ are placed at the vertices $$A$$ and $$B$$ of an equilateral triangle $$A B C$$. A third body of mass $$2 \mathrm{~kg}$$ is placed at the centroid $$G$$ of the triangle. If $$A G=B G=C G=1 \mathrm{~m}$$, where should a fourth body of mass $$4 \mathrm{~kg}$$ be placed, so that the resultant force on the $$2 \mathrm{~kg}$$ body is zero?

The value of acceleration due to gravity at a height of $$10 \mathrm{~km}$$ from the surface of earth is $$x$$. At what depth inside the earth is the value of the acceleration due to gravity has the same value $$x$$ ?

A satellite is orbiting close to the earth and has a kinetic energy $$K$$. The minimum extra kinetic energy required by it just overcome the gravitation pull of the earth is