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A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the figure. A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if $2 r < x < 2 R$ .

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A

$\frac{G m m ^{'}}{4 ( x - x ) ^{2}}$

B

$\frac{G m m ^{'}}{( x - r ) ^{2}}$

C

$\frac{G m m ^{'}}{( x - r ) ^{3}}$

D

$\frac{2 G m m ^{'}}{( x - r ) ^{2}}$

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Correct option is B)

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