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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationSatellite MotionEasy2 minPYQ_2020

PhysicsEasysingle choice

A projectile is fired from the surface of the Earth of radius $R$ with a velocity $η v_{e}$ , where $v_{e}$ is the escape velocity and $η < 1$ . Neglecting the air resistance, the orbital velocity of the projectile is

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Answer:

Solution:

Velocity at the surface $= v_{s} = η v_{e}$

Velocity in orbit $= v_{0}$

By conversation of mechanical energy,

$\frac{1}{2} m v_{s}^{2} + (- \frac{G M m}{R}) = \frac{1}{2} m v_{0}^{2} - \frac{G M m}{r} \dots (1)$

By Newton's law, $\frac{G M m}{r^{2}} = \frac{m v_{0}^{2}}{r} \dots (2)$

Solving equations (1) and (2)

$v_{0} = v_{e} \sqrt{1 - η^{2}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:GravitationSubtopic:Satellite Motion

⏱ 2mℹ️ Source: PYQ_2020

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