Question

Infinite bodies, each of mass 3kg are situated at distances 1m, 2m, 4m,8m....... respectively on x-axis. The resultant intensity of gravitational field at the origin will be

• A. G
• B. 2G
• C. 3G
• D. 4G

Answer 1

Answer: (D)

4G

Answer 2

Intensity at the origin $I = I _ { 1 } + I _ { 2 } + I _ { 3 } + I _ { 4 } + \ldots \ldots$

$= G M \left( \frac { 1 } { 1 - \frac { 1 } { 4 } } \right)$

[As sum of G.P. $= \frac { a } { 1 - r }$ ]

$= G M \times \frac { 4 } { 3 }$ $= G \times 3 \times \frac { 4 } { 3 } = 4 G$ [As $M = 3 \mathrm {~kg}$ given]