question_answer

Masses of 1 kg each are placed 1 m, 2 m, 4 m, 8 m, ..... from a point P. The gravitational field intensity at P due to these masses is

A) \[G\]                 

B)        \[G\]

C) \[4G\]               

D)        \[\frac{4G}{3}\]

Correct Answer: D

Solution :

[d] \[E=\frac{G\times 1}{{{1}^{2}}}+\frac{G\times 1}{{{2}^{2}}}+\frac{G\times 1}{{{4}^{2}}}+...+\] \[E=G\left[ 1+\frac{1}{4}+\frac{1}{16}+... \right]\] \[E=G\frac{1}{1-\frac{1}{4}}=\frac{4G}{3}\]