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 earths 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 \[w=mg=\frac{4}{9}mg=\frac{4}{9}w.\]