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Weight of an object is $294 \mathrm{~N}$ on the surface of the earth. What is its weight at a height of $200 \mathrm{~km}$ from the surface of the earth. Radius of the earth $=6400 \mathrm{~km}$.

Solution-

Weight at a height of $200 \mathrm{~km}$

$W_{h}=m g_{h}=m g\left(\frac{R}{R+h}\right)^{2} \quad\left[\because g_{h}=g\left(\frac{R}{R+h}\right)^{2}\right]$

Here $m g=294 \mathrm{~N}, R=6400 \mathrm{~km}, h=200 \mathrm{~km}$

\begin{aligned} \therefore W_{h} &=294\left[\frac{6400}{6400+200}\right]^{2} \\ &=294\left[\frac{6400}{6600}\right]^{2}=276.45 \mathrm{~N} \end{aligned}

So the : Weight decreases with increase in height from the surface of the earth.

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