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The escape velocity of a body on a planet A is 12 km s-1. The escape velocity of the body on another planet B, whose density is four times and radius is half of the planet A, is 

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Important Questions on Gravitation

EASY
JEE Main
IMPORTANT
The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be
MEDIUM
JEE Main
IMPORTANT
Three identical particle A,B and C of mass 100 kg each are placed in a straight line with AB=BC=13 m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13 m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately
EASY
JEE Main
IMPORTANT
An object is taken to a height above the surface of earth at a distance 54R from the centre of the earth. Where radius of earth, R=6400 km. The percentage decrease in the weight of the object will be
EASY
JEE Main
IMPORTANT
The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be
(Radius of earth =6400 km)
HARD
JEE Main
IMPORTANT
A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be
(Take radius of earth =6400 km and g=10 ms-2)
MEDIUM
JEE Main
IMPORTANT
Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is 
MEDIUM
JEE Main
IMPORTANT
A body of mass m is projected with velocity λve in vertically upward direction from the surface of the earth into space. It is given that ve is escape velocity and λ<1. If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be (R : radius of earth)
EASY
JEE Main
IMPORTANT
If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately