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Question

Match the following.

Solution
Verified by Toppr

Part A
We know,
Escape Velocity=2GMpRp (Mp= mass of planet).
Here Escape Velocity is independent of mass of body,
direction of propagation,and temperature of planet.
Hence A1,3,5

Part B
Atmosphere exists when the air molecules can't escape the
planets gravitational force.
Hence, existence of atmosphere on a planet also depends upon the
escape velocity of the planet, but is independent of the mass of the planet.
And the temperature of the planet.
And existence of atmosphere has no reference with mass of body or mass of body, so we have nothing to do with these options.
Hence B2,4,5

Part C
Acceleration due to gravity(g)=GMpR2 (Mp= mass of planet.)
It is independent of the mass of body upon which the acceleration is acting,
Whatever may be the direction of propagation but the value of g is same,
also it is independent of temperature of the planet.
But g depends on the escape velocity of the planet,as g=v2R
Hence C1,3,5

Part D
Potential Energy of planet mass system=GMpmR
It is clear that it us independent of direction of propagation of the body,and the temperature of the planet.
Hence D1,5

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