Question

An infinite number of masses, each of one kg are placed on the +ve X axis at 1m, 2m, 4m ________ from the origin. The magnitude of the gravitational field at origin due to this distribution of masses is

• A. $2G$
• B. $\frac{4G}{3}$
• C. $\frac{3G}{4}$
• D. $\infty$

Answer 1

The correct option is B $\frac{4G}{3}$

The magnitude of gravitational field intensity at origin will be the sum of gravitational

field intensity due to each mass m = 1 Kg,

So, intensity $\left(I\right)=Gm(\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}...)$

Now putting $r_1=1,r_2=2,r_3=4$ and so on and m = 1

We get

$I=G(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{4^2}...)$

Since it is a GP, so by using formula for sum of GP

We get,

$I=G\left(\frac{1}{1-\frac{1}{2^2}}\right)|$

$\Rightarrow I=\frac{4G}{3}$