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JEE Main202127 Jul 2021Morning ShiftPhysicsGravitationActual

Suppose two planets (spherical in shape) of radii R and 2 R , but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass m is projected from the surface of the planet of mass M directly towards the centre of the second planet. The minimum speed v required for the satellite to reach the surface of the second planet is a 7 G M R , then the value of a is [Given : T

Correct answer

0

Step-by-step solution

Acceleration due to gravity will be zero at P therefore, G M x 2 = G 9 M ( 8 R - x ) 2 8 R - x = 3 x x = 2 R Apply conservation of energy and consider velocity at P is zero. 1 2 m v 2 - G M m R - G 9 M m 7 R = 0 - G M m 2 R - G 9 M m 6 R ∴   V = 4 7 G M R

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