A tunnel is dug along a chord of the earth at a perpendicular distance $\frac{R}{3}$ from the earth's centre. Assume wall of the tunnel is frictionless. Find the force exerted by the wall on mass m at a distance x from the centre of the tunnel

\frac{m g \sqrt{\frac{R^{2}}{9} + x^{2}}}{R}

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\frac{m g x}{\sqrt{R^{2} / a + x^{2}}}

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\frac{m g}{3}

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\frac{m g x}{R}

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Solution

The correct option is B $\frac{m g}{3}$
$F = m g^{'} = m g ⎡ ⎢ ⎢ ⎣ 1 + \frac{\sqrt{\frac{R^{3}}{9} + x^{2}}}{9} ⎤ ⎥ ⎥ ⎦$
$= \frac{m g \sqrt{R^{2} / 9 + x^{2}}}{R} . \frac{R / 3}{\sqrt{R^{2} / 9 + x^{2}}} = \frac{m g}{3}$

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A tunnel is dug along a chord of the earth at a perpendicular distance R3 from the earth's centre. Assume wall of the tunnel is frictionless. Find the force exerted by the wall on mass m at a distance x from the centre of the tunnel

The correct option is B mg3F=mg′=mg⎡⎢ ⎢⎣1+√R39+x29⎤⎥ ⎥⎦=mg√R2/9+x2R.R/3√R2/9+x2=mg3

A tunnel is dug along a chord of the earth at a perpendicular distance $\frac{R}{3}$ from the earth's centre. Assume wall of the tunnel is frictionless. Find the force exerted by the wall on mass m at a distance x from the centre of the tunnel

The correct option is B $\frac{m g}{3}$
$F = m g^{'} = m g ⎡ ⎢ ⎢ ⎣ 1 + \frac{\sqrt{\frac{R^{3}}{9} + x^{2}}}{9} ⎤ ⎥ ⎥ ⎦$
$= \frac{m g \sqrt{R^{2} / 9 + x^{2}}}{R} . \frac{R / 3}{\sqrt{R^{2} / 9 + x^{2}}} = \frac{m g}{3}$