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Two concentric shells of masses M1 and M2 are having radii r1 and r2. Which of the following is the correct expression for the gravitational field at a distance r.

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Important Questions on Gravitation

EASY
JEE Advanced
IMPORTANT
The radius of a planet is R. A satellite revolves around it in a circle of radius r with angular velocity ω0. The acceleration due to the gravity on planet's surface is
MEDIUM
JEE Advanced
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A space vehicle approaching a planet has a speed v, when it is very far from the planet. At that moment tangent of its trajectory would miss the centre of the planet by distance R. If the planet has mass M and radius r, what is the smallest value of R in order that the resulting orbit of the space vehicle will just miss the surface of the planet?
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JEE Advanced
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A solid sphere of radius R/2 is cut out of a solid sphere of radius R such that the spherical cavity so formed touches the surface on one side and the centre of the sphere on the other side, as shown. The initial mass of the solid sphere was M. If a particle of mass m is placed at a distance 2.5 R from the centre of the cavity, then what is the gravitational attraction on the mass m ?

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JEE Advanced
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Abody is released from a point of distance R' from the centre of earth. Its velocity at the time of striking the earth will be R'>Re
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JEE Advanced
IMPORTANT

A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F1 un a particle placed at a distance 2R 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 the cavity now applies a gravitational force F2 on the same particle. The ratio F1/F2 is

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EASY
JEE Advanced
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Consider two solid uniform spherical objects of the same density ρ. One has radius R and the other has radius 2 R. They are in outer space where the gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?
EASY
JEE Advanced
IMPORTANT
A body starts from rest from a point distant r0 from the centre of the earth. It reaches the surface of the earth whose radius is R. The velocity acquired by the body is
EASY
JEE Advanced
IMPORTANT
Suppose the gravitational force varies inversely as the nth  power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to