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  • The fractional change in the value of free-fall acceleration ‘g’ for a particle when it is lifted from the surface to an elevation h <img alt="\mathrm{(h<<R) \text { is }}" src="h

The fractional change in the value of free-fall acceleration ‘g’ for a particle when it is lifted from the surface to an elevation h \mathrm{(h<<R) \text { is }}

Option: 1

\mathrm{\frac{h}{R}}


Option: 2

\mathrm{-\frac{2 h}{R}}


Option: 3

\mathrm{\frac{2 h}{R}}


Option: 4

none of these.


Answers (1)

best_answer

\mathrm{\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2} \quad \ldots \ldots \text { (i) }}

\mathrm{\frac{d g}{d R}=\frac{-2 G M}{R^3} \quad \text { putting } d R=h \text { we obtain }}

\mathrm{\Rightarrow \frac{d g}{h}=\frac{-2 G M}{R^2} \cdot \frac{1}{R} \quad \ldots \text { (ii) }}

From (i) and (ii)

\mathrm{\Rightarrow \frac{\mathrm{dg}}{\mathrm{g}}=-2\left(\frac{\mathrm{h}}{\mathrm{R}}\right)}

\mathrm{\Rightarrow \text { Change is }-v e \text {. That means } g \text { decreases. }}

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Ritika Jonwal

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