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Density of planet is two times the density of earth Radius of this to earth) Match the following

Table – 1 Table – 2
(A) Acceleration due to gravity on this planet’s surface (P) Half
(B) Gravitational potential on the surface (Q) same
(C) Gravitational potential at centre (R) Two times
(D) Gravitational field strength at centre

(S) four time

1 Answer

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Best answer

A-Q,   

B-P,   

C-P,   

D-Q

(A) in terms of density g = (4/3)πρ GR i.e. g ∝ ρR

given :  ρ1 = 2ρ

R1 = (R/2)

hence (g / g') = (ρR / ρ1R1)

∴  (g / g') = [ρR / {2ρ × (R/2)}] = 1

g = g'

i.e. acceleration due to gravity remains same

(B) Gravitational Potential ∝ distance

hence if planet is having half radius, then gravitational potential on the surface will also be half. 

(C) Similarly gravitational potential at centre will be half of that for earth centre. 

(D) Gravitational field strength remains unchanged.

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