MEDIUM
JEE Advanced
IMPORTANT
Earn 100

Two bodies, each of mass , are kept fixed with a separation of . A particle of mass is projected from the midpoint of the line joining their centers, perpendicular to the line. The gravitational constant is . The correct statement (s) is (are) :
(a)The minimum initial velocity of the mass to escape the gravitational field of the two bodies is .
(b)The minimum initial velocity of the mass to escape the gravitational field of the two bodies is .
(c)The minimum initial velocity of the mass to escape the gravitational field of the two bodies is .
(d)The energy of the mass does not remains constant.

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Important Questions on Gravitation
HARD
JEE Advanced
IMPORTANT
Consider a spherical gaseous cloud of mass density in free space where is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy . The force acting on the particles is their mutual gravitational force. If is constant in time, the particle number density is: [ is universal gravitational constant]
