The magnitude of the potential energy per unit mass of the object at the surface of earth is E. Then the escape velocity of the object is

A small ball of mass ‘m’ is released at a height ‘R’ above the earth surface, as shown in the figure above. If the maximum depth of the ball to which it goes is R/2 inside the earth through a narrow grove before coming to rest momentarily. The grove, contain an ideal spring of spring constant K and natural length R, find the value of K if R is radius of earth and M mass of earth

The escape velocity for a planet is v_e A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

The figure shows the variation of energy with the orbit radius of a body in circular planetary motion. Find the correct statement about the curves A, B and C

The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is The value of orbital velocity for another satellite orbiting at an altitude of half of earth’s radius is

A particle starts from rest at a distance R from the centre and along the axis of a fixed ring of radius R & mass M. Its velocity at the centre of the ring is

Two identical spherical balls each of mass m are placed as shown in figure. Plot the variation of g(gravitation intensity) along the x-axis

A particle of mass M is at a distance a from surface of a thin spherical shell of equal mass and having radius a.

A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F₁ on a particle placed at a distance 3R from the centre of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in the figure. The sphere with cavity now applies a gravitational force F2 on the same particle. The ratio F₂ /F₁ is

Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has same mass. Length of the rod is R, where R is the radius of earth

At what height above the earth’s surface does the acceleration due to gravity fall to 1% of its value at the earth’s surface?

Two concentric shells of uniform density of mass M₁ and M₂ are situated as shown in the figure. The forces experienced by a particle of mass m when placed at positions A, B and C respectively are (given OA = p, OB = q and OC = r)

With what angular velocity the earth should spin in order that a body lying at 30° latitude may become weightless [R is radius of earth and g is acceleration due to gravity on the surface of earth]

A man of mass m starts falling towards a planet of mass M and radius R. As he reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass and a point mass at the center. Change in the force of gravity experienced by the man is

Man outside the shell is 2GMm/3R^2

If the radius of the earth be increased by a factor of 5, by what factor its density be changed to keep the value of g the same?

A spherical hole of radius R/2 is excavated from the asteroid of mass M as shown in fig. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is