SATHEE: Gravitation Question 225

Gravitation Question 225

Question: In a cosmic event, suppose a planet heavier than the earth with mass KM (K > 1) and radius K’R (K > 1) passes through a path near the earth (M and R are the mass and radius of earth). At what closest distance from surface of planet, we are in danger ofbeing thrown into space:

Options:

A) $[{[\frac{2 K G M}{g}]}^{1 / 2} - \frac{1}{2} K^{'} R]$

B) $[{[\frac{K G M}{2 g}]}^{1 / 2} - \frac{1}{2} K^{'} R]$

C) $[{[\frac{K G M}{g}]}^{1 / 2} - \frac{1}{2} K^{'} R]$

D) $[{[\frac{K G M}{g}]}^{1 / 2} - K^{'} R]$

Show Answer

Answer:

Correct Answer: D

Solution:

we will be thrown into space, if weight mg is equal to gravitational force duet to the planet. If y is the closest distance. $[\frac{G M m}{R^{2}} = m g = \frac{G (K M) m}{{(K^{'} R + y)}^{2}}]$ $[{(K^{'} R + y)}^{2} = \frac{K G M}{g}]$ $[y = {(\frac{K G M}{g})}^{1 / 2} - K^{'} R]$

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Gravitation Question 225

Question: In a cosmic event, suppose a planet heavier than the earth with mass KM (K > 1) and radius K’R (K > 1) passes through a path near the earth (M and R are the mass and radius of earth). At what closest distance from surface of planet, we are in danger ofbeing thrown into space:

Options:

Answer:

Solution:

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