A small block of superdense material has mass 2 × 1 0 24 k g . It is at a height h < < R . It falls towards the earth. Find its speed when it is at a height h 2 .

Mass of earth is, M = 6 × 1 0 24 k g Mass of superdense material m = 2 × 1 0 24 kg = M 3 From momentum conservation, M V 1 = M 3 V 2 From energy conservation V 1 = V 2 3 1 2 M V 1 2 + 1 2 M 3 V 2 2 = G M M 3 h 2 + R - G M M 3 h + R ∴ v 2 = 3 g h 4

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PhysicsGravitationEnergy & PotentialEasy2 minPYQ_2020

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A small block of superdense material has mass $2 \times 1 0^{24} k g$ . It is at a height $h < < R$ . It falls towards the earth. Find its speed when it is at a height $\frac{h}{2}$ .

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Answer:

Solution:

Mass of earth is, $M = 6 \times 1 0^{24} k g$

Mass of superdense material $m = 2 \times 1 0^{24} kg = \frac{M}{3}$

From momentum conservation, $M V_{1} = \frac{M}{3} V_{2}$

From energy conservation $V_{1} = \frac{V_{2}}{3}$

$\frac{1}{2} M V_{1}^{2} + \frac{1}{2} (\frac{M}{3}) V_{2}^{2} = \frac{G M (\frac{M}{3})}{\frac{h}{2} + R} - \frac{G M (\frac{M}{3})}{h + R}$

$∴ v_{2} = \sqrt{\frac{3 g h}{4}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:GravitationSubtopic:Energy & Potential

⏱ 2mℹ️ Source: PYQ_2020

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