Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationEnergy & PotentialEasy2 minPYQ_2018

PhysicsEasysingle choice

An asteroid of mass $m$ is approaching earth, initially at a distance $10 R_{e}$ with speed $v_{i} .$ It hite oarth with a speed $v_{f},$ $(R_{e}$ and $M_{e}$ are radius and mass of earth $)$ , then

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Solution:

Initial energy of the asteroid is
$E_{i} = K_{i} + U_{i} = \frac{1}{2} m v_{i}^{2} - \frac{G M_{θ} m}{10 R_{e}}$

Final energy of the asteroid,
$E_{f} = \frac{1}{2} m v_{f}^{2} - \frac{G M_{θ} m}{R_{θ}}$

According to law of conservation of energy, $E_{i} = E_{f}$

$\frac{1}{2} m v_{i}^{2} - \frac{G M_{θ} m}{10 R_{θ}} = \frac{1}{2} m v_{f}^{2} - \frac{G M_{θ} m}{R_{θ}}$

$v_{f}^{2} - \frac{2 G M_{θ}}{R_{θ}} = v_{i}^{2} - \frac{2 G M_{θ}}{10 R_{θ}}$

$\Rightarrow v_{f}^{2} = v_{i}^{2} + \frac{2 G M_{θ}}{R_{θ}} (1 - \frac{1}{10})$

Stream:BITSATSubject:PhysicsTopic:GravitationSubtopic:Energy & Potential

⏱ 2mℹ️ Source: PYQ_2018

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