Shell it out

Classical Mechanics Level 2

A green sphere of mass $m_b$ is placed inside a spherical shell of radius $R$ and mass $M_s$ . Two spheres identical in mass to the green sphere are placed a distance $d$ to the right and to the bottom, respectively, of it. What is the magnitude of the gravitational force on the green sphere?

\sqrt{2}\frac{Gm_b^2}{d^2}

\sqrt{2}\frac{Gm_b^2}{d^2} + \frac{Gm_bM_s}{R^2}

2\frac{Gm_b^2}{d^2} + \frac{Gm_bM_s}{R^2}

2\frac{Gm_b^2}{d^2}

2 solutions

Anandhu Raj
Dec 27, 2014

Gravitational force on a point mass inside a uniform spherical shell is zero.

Gravitational force between A and B = $\frac{Gm_{b}^2}{d^2}$ $\overset{\^}{i}$

Gravitational force between A and C = $\frac{Gm_{b}^2}{d^2}$ $\overset{\^}{j}$

Taking vector sum, magnitude of total gravitational force experienced by the green Sphere = $\displaystyle\frac{\sqrt{2}Gm_{b}^2}{d^2}$

Nishant Sharma
Dec 14, 2014

Since gravitational force on a point mass inside a uniform spherical shell is zero so we have net force on the mass as $\displaystyle\frac{\sqrt{2}Gm_{b}^2}{d^2}$ .

Shell it out

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