question_answer

A body weighs w newton at the surface of the earth. Its weight at a height equals to half the radius of the earth, will be

A) \[\frac{w}{2}\]                                 

B) \[\frac{2w}{3}\]

C) \[\frac{4w}{9}\]                                               

D)  \[\frac{8w}{27}\]

Correct Answer: C

Solution :

The value of acceleration due to gravity at a height \[h\] above the earth's surface is given by                 \[g'=\frac{g}{{{\left( 1+\frac{h}{R} \right)}^{2}}}\] where \[R\] is radius, of earth When    \[h=\frac{R}{2}\]                 \[g'=\frac{g}{{{\left( 1+\frac{1}{2} \right)}^{2}}}\]                     \[=\frac{4g}{9}\] Hence, weight\[w'=mg'=\frac{4}{9}mg=\frac{4}{9}w\].