Two concentric shells of uniform density of m | vedclass

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(D) According to the shell theorem,the gravitational force inside a uniform spherical shell is zero,and the force outside is equivalent to the entire

Vedclass · Accepted Answer

$G\frac{(M_1 + M_2)m}{p^2}, G\frac{M_1 m}{q^2}$ and zero

Vedclass · Answer

(D) According to the shell theorem,the gravitational force inside a uniform spherical shell is zero,and the force outside is equivalent to the entire mass being concentrated at the center.$1$. At position $A$ (outside both shells): The distance from the center $O$ is $p$. The total mass is $M_1 + M_2$. The force is $F_A = G\frac{(M_1 + M_2)m}{p^2}$.$2$. At position $B$ (between the two shells): The distance from the center $O$ is $q$. The particle is outside shell $M_1$ but inside shell $M_2$. The force due to $M_2$ is zero. The force due to $M_1$ is $F_B = G\frac{M_1 m}{q^2}$.$3$. At position $C$ (inside both shells): The distance from the center $O$ is $r$. The particle is inside both shells $M_1$ and $M_2$. Therefore,the net gravitational force is $F_C = 0$.

Two concentric shells of uniform density of mass $M_1$ and $M_2$ are situated as shown in the figure. The forces experienced by a particle of mass $m$ when placed at positions $A, B$ and $C$ respectively are (given $OA = p, OB = q$ and $OC = r$):

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