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(A) The acceleration due to gravity at a height $h$ above the earth's surface is given by the formula:$g^{\prime} = g \left( \frac{R}{R+h} \right)^{2}

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$(n+1)^{2}$

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(A) The acceleration due to gravity at a height $h$ above the earth's surface is given by the formula:$g^{\prime} = g \left( \frac{R}{R+h} \right)^{2}$Given that the height $h = nR$,we substitute this into the equation:$g^{\prime} = g \left( \frac{R}{R+nR} \right)^{2}$$g^{\prime} = g \left( \frac{R}{R(1+n)} \right)^{2}$$g^{\prime} = g \left( \frac{1}{1+n} \right)^{2}$Now,we find the ratio of the acceleration due to gravity on the surface $(g)$ to that at the altitude $(g^{\prime})$:$\frac{g}{g^{\prime}} = \frac{g}{g \left( \frac{1}{1+n} \right)^{2}}$$\frac{g}{g^{\prime}} = (1+n)^{2}$Therefore,the ratio is $(n+1)^{2}$.

$A$ body is taken to a height of $n R$ from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is

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