Qstnid -Iv-10-two Concentric Spherical Shells Have Masses M<sub>1</sub>, M<sub>2</sub> And Radii R<sub>1</sub>, R<sub>2</sub> (R<sub>1</sub> &Lt; R<sub>2</sub>). What Is The Force Exerted By This System On A Particle Of Mass M<sub>1</sub> If It Is Placed At A Distance (R<sub>1</sub> + R<sub>2</sub>)/2 From The Centre? - 11: Gravitation - Neet-xii-physics

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NEET-XII-Physics

11: Gravitation

with Solutions - page 5

Qstn# iv-10 Prvs-Qstn Next-Qstn

#10
Two concentric spherical shells have masses M₁, M₂ and radii R₁, R₂ (R₁ < R₂). What is the force exerted by this system on a particle of mass m₁ if it is placed at a distance (R₁ + R₂)/2 from the centre?
Ans : Consider that mass m is at a distance `` \frac{{R}_{1}+{R}_{2}}{2}`` as shown in the figure.

The gravitational force of m due to the shell of M₂ is zero, because the mass is inside the shell.
∴ Gravitational force due to the shell of mass M₂ = `` \frac{G{M}_{1}m}{{\left({\displaystyle \frac{{R}_{1}+{R}_{2}}{2}}\right)}^{2}}=\frac{4G{M}_{1}m}{{\left({R}_{1}+{R}_{2}\right)}^{2}}``
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