Physics - Gravitation Question with Solution | TestHub

PhysicsGravitation615Medium2 minQB

PhysicsMediumnumerical

Passage / Comprehension

Since gravitational field is conservative, we can conserve the total mechanical energy of the system of interacting particles. As the net force acting on a closed system is zero, we can conserve the linear momentum of the system. Since the gravitational forces between two interacting particles are action-reaction pair, the net torque experienced by the system about any inertial point is zero. Hence, angular momentum of the system remains constant about any inertial point. A body of mass $m (≪ M)$ is projected tangentially to earth's surface with a speed $v_{0} = \frac{4 GM}{3 R}$ .

The maximum height attained by the body is $λ$ R. find $λ$ .

Answer:

1.00

Solution:

Conservation of energy and angular momentum:

$\frac{1}{2} m v_{0}^{2} - \frac{GM m}{R}$

$= \frac{1}{2} m v^{2} - \frac{GM m}{R + h}$

with

$m v_{0} R = m v (R + h)$

Using

$v_{0}^{2} = \frac{4 GM}{3 R}$

gives h = R, so

$λ = 1$

Answer 1.00

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:615

⏱ 2mℹ️ Source: QB

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