Question

A particle weighs $120\text{N}$ on the surface of the earth. At what height above the earth's surface will its weight be $30\text{N}$?

Radius of the earth $=6400\text{km}$

• A. $6400\text{km}$
• B. $3200\text{km}$
• C. $1600\text{km}$
• D. $1800\text{km}$

Answer 1

The correct option is A $6400\text{km}$

Suppose, the height be $h$ from the surface of the earth, at which weight is $30\text{N}$.

Given,

$120=\frac{GMm}{R^2}...\left(i\right)$

$30=\frac{GMm}{(R+h{)}^2}...\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$,

$R+h=2R$

$\Rightarrow h=R=6400\text{km}$