A spherical planet has a mass Mp and diameter Dp. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

Question

A spherical planet has a mass Mp and diameter Dp. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to (A)  (4GMp/Dp2)  (B)  (GMpm/Dp2)  (C)  (GMp/Dp)  (D)  (4GMpm/Dp2)

Tardigrade Admin · Accepted Answer

Gravitational force acting on particle of mass m is F=(G Mp m/(Dp / 2)2) Acceleration due to gravity experience by the particle is g=(F/m)=(G Mp/(Dp / 2)2)=(4 G Mp/Dp2)

Q. A spherical planet has a mass $M_{p}$ and diameter $D_{p}$ . A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

$\frac{4 G M _{p}}{D _{p}^{2}}$

$\frac{G M _{p} m}{D _{p}^{2}}$

$\frac{G M _{p}}{D _{p}}$

$\frac{4 G M _{p} m}{D _{p}^{2}}$

Gravitational force acting on particle of mass $m$ is
$F = \frac{G M _{p} m}{( D _{p} /2 ) ^{2}}$
Acceleration due to gravity experience by the particle is
$g = \frac{F}{m} = \frac{G M _{p}}{( D _{p} /2 ) ^{2}} = \frac{4 G M _{p}}{D _{p}^{2}}$

Q. A spherical planet has a mass Mp​ and diameter Dp​. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

Dp2​4GMp​​

Dp2​GMp​m​

Dp​GMp​​

Dp2​4GMp​m​