First slide

Gravitational field intensity

Question

An infinite number of particles each of mass 1kg are placed on the positive x-axis at 1m, 2m, 4m, 8m…. from the origin. The magnitude of the resultant gravitational force on 1kg mass kept at the origin is

Moderate

A

0
B

G
C

3G/4
D

4G/3

Solution

$\large F = G{\left( m \right)^2}\left[ {\frac{1}{1} + \frac{1}{{{2^2}}} + \frac{1}{{{4^2}}} + \frac{1}{{{8^2}}} + ......} \right]$
$\large F = G{\left( 1 \right)^2}\left( {\frac{1}{{1 - \frac{1}{4}}}} \right) = \frac{{4G}}{3}$

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