A uniform thin rod of mass m and length R is placed normally on surface of earth as shown. The mass of earth is M and its radius is R. Then the magnitude of gravitational force exerted by earth on the rod is?

\frac{G M m}{2 R^{2}}

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\frac{G M m}{4 R^{2}}

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\frac{4 G M m}{9 R^{2}}

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\frac{G M m}{8 R^{2}}

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Solution

The correct option is A $\frac{G M m}{2 R^{2}}$
$d F = \frac{G M d m}{({R + x}^{2})}$
$d M = \frac{m d x}{R}$
$d F = \frac{G M m d x}{R ({R + x}^{2})}$
$F = \frac{G M m}{{2 R}^{2}}$
integrating wrt x in limit 0 to R

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A uniform thin rod of mass m and length R is placed normally on surface of earth as shown. The mass of earth is M and its radius is R. Then the magnitude of gravitational force exerted by earth on the rod is?

The correct option is A GMm2R2dF=GMdm(R+x2)dM=mdxRdF=GMmdxR(R+x2)F=GMm2R2integrating wrt x in limit 0 to R

The correct option is A $\frac{G M m}{2 R^{2}}$
$d F = \frac{G M d m}{({R + x}^{2})}$
$d M = \frac{m d x}{R}$
$d F = \frac{G M m d x}{R ({R + x}^{2})}$
$F = \frac{G M m}{{2 R}^{2}}$
integrating wrt x in limit 0 to R