Question

Calculate the mass and weight of the object which is at height of twice the radius of the Earth from the surface of the Earth, if mass and weight of the object is $m$ and $w$ respectively.

• A. its mass is $\frac{m}{2}$ and its weight is $\frac{w}{2}$
• B. its mass is $m$ and its weight is $\frac{w}{8}$
• C. its mass is $\frac{m}{2}$ and its weight is $\frac{w}{4}$
• D. its mass is $m$ and its weight is $\frac{w}{4}$
• E. its mass is $m$ and its weight is $\frac{w}{9}$

Answer 1

Answer: (E)

its mass is $m$ and its weight is $\frac{w}{9}$

Weight of the object at the surface$=w=\frac{GMm}{R^2}$

Mass of the object is universally constant. Thus it remains $m$ everywhere.

The weight of the object at height $h=2R$,

$F=\frac{GMm}{(h+R{)}^2}=\frac{GMm}{9R^2}=\frac{w}{9}$