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

A steady flow of water passes along a horizontal tube from a wide section X to the narrower section Y, see figure. Manometers are placed at P and Q at the sections. Which of the statements A, B, C, D, E is most correct?

A cylindrical vessel is filled with a liquid up to height H. A small hole is made in the vessel at a distance y below the liquid surface as shown in figure. The liquid emerging from the hole strike the ground at distance x

A tank is filled upto a height h with a liquid and is placed on a platform of height h from the ground. To get maximum range x_m a small hole is punched at a distance of y from the free surface of the liquid. Then

Figure shows a siphon. Choose the wrong statement