Question

The weight of a body is 392N on the surface of the earth. What is the weight if this body at a height of 100 km? Given radius of the earth is 6400km.​

Answer 1

GIVEN:-

• $\tt{Weight\:of\:the\:Body=392N}$

• $\tt{Radius\:of\:the\:earth=6400km}$

• $\tt{g=9.8m/s^-2}$

TO FIND:-

• Value of 'g' at the height 'h'

• The weight of this body at the height of 100km.

FORMULAE USED:-

The value of 'g' at height h is given by

• ${\boxed{\tt{g_h=g(\dfrac{R_e}{R_e+h})^2}}}$

Now,

$\implies\tt{g_h=9.8m/s^-2\times{(\dfrac{6400km}{(6400+100)km})^2}}$

$\implies\tt{g_h=9.8m/s^-2\times{(\dfrac{6400}{6500})^2}}$

$\implies\tt{g_h=9.8m/s^-2\times{\dfrac{4096}{4225}}}$

$\implies\tt{g_h=9.5m/s^2}$

Hence,

Weight of the body at height of 100km

$\implies\tt{Weight_gh=mg_h}$

$\implies\tt{Weight=40kg×9.5m/s^-2}$

$\implies\tt{Weight=380N}$

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