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Units and Dimensions

Rate of chang...

Question

Rate of change of weight near the earth's surface varies with height h (h<<R where R is the radius of the Earth) as

A

h

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B

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C

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D

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Solution

The correct option is B

g(h) = g $(1 - \frac{2 h}{R})$ (h<<R)

Rate of change of weight with height

= $∣ ∣ \frac{d W}{d h} ∣ ∣$ = $∣ ∣ \frac{d (m g)}{d h} ∣ ∣$ = m $∣ ∣ \frac{d (g)}{d h} ∣ ∣$

= $\frac{2 m g}{R}$ = constant

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