Mass density of a planet varies as ρ ( r ) = R ρ 0 r ; where R is radius of planet and r is distance from center of planet :-

Mass of planet: M = ∫ ρ d V = ∫ r = 0 R R ρ 0 r × 4 π r 2 d r M = π ρ 0 R 3 (A) 2 1 m v e 2 − R GM m = 0 v e = R 2 GM = 2 π G ρ 0 R 2 (C) E = R 2 GM = π G ρ 0 R (D) V 0 = R GM = π ρ 0 G R 2 T = V 0 2 π R

Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceMedium2 minQB

PhysicsMediummultiple choice

Mass density of a planet varies as $ρ (r) = \frac{ρ _{0} r}{R}$ ; where R is radius of planet and r is distance from center of planet :-

Options:(select one or more)

Answer:

A, C

Solution:

Mass of planet: $M = \int ρ d V = \int_{r = 0}^{R} \frac{ρ _{0} r}{R} \times 4 π r^{2} d r$ $M = π ρ_{0} R^{3}$

(A)

$\frac{1}{2} m v_{e}^{2} - \frac{GM m}{R} = 0$

$v_{e} = \frac{2 GM}{R} = 2 π G ρ_{0} R^{2}$

(C)

$E = \frac{GM}{R ^{2}} = π G ρ_{0} R$

(D) $V_{0} = \frac{GM}{R} = π ρ_{0} G R^{2}$

$T = \frac{2 π R}{V _{0}}$

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: QB

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