If the gravitational force had varied as r^–5/2 instead of r^–2;the potential energy of a particle at a distance ‘r’from the centre of the earth would be proportional to

The radius of a planet is 1/4^th of R_e and its acc. due to gravity is 2g. What would be the value of escape velocity on the planet, if escape velocity on earth is v_e.

What would be the length of a sec. pendulum at a planet(where acc. due to gravity is g/4) if it’s length on earth is l

If the mass of earth is eighty times the mass of a planet and diameter of the planet is one fourth that of earth, then acceleration due to gravity on the planet would be

The mass of the moon is 1/81 of earth’s mass and its radius 1/4 that of the earth. If the escape velocity from the earth’s surface is 11.2 km/sec, its value from the surface of the moon will be

A planet of mass 3 × 10²⁹ gm moves around a star with aconstant speed of 2 × 10⁶ ms^–1 in a circle of radii 1.5 × 10¹⁴cm. The gravitational force exerted on the planet by the star is

Taking the gravitational potential at a point infinte distance awayas zero, the gravitational potential at a point A is –5 unit. If the gravitational potential at point infinite distance away is taken as + 10 units, the potential at point A is

Two planets of radii r₁ and r₂ are made from the same material. The ratio of the acceleration due to gravity g₁/g₂ at the surfaces of the two planets is

The weight of an object in the coal mine, sea level and at the top of the mountain,are respectively W₁, W₂ and W₃ then

A planet moves around the sun. At a point P it is closest from the sun at a distance d₁ and has a speed v₁. At another point Q, when it is farthest from the sun at a distnace d₂ its speed will be