Infinite number of bodies each of mass 2kg

Asked by admin @ 29/08/2021 in Physics viewed by 280 People

infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m, 4m, 8m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be 1. g 2. 3. 4. 4g

Answered by admin @ 29/08/2021

Answer:

-4G

Step by step explanation:

The gravitational potential due to a mass 'M' at a distance 'd' from it is:

$V=\frac{-GM}{d}$ .

Since there are infinite number of masses, therefore, the total gravitational potential is:

$-[\frac{GM}{1}+\frac{GM}{2}+\frac{GM}{4}+..... \infty]\\ \\=-GM[1+\frac{1}{2}+\frac{1}{4}=.....\infty]\\ \\=-2G[1+\frac{1}{2}+\frac{1}{2^2}+.... \infty] \\ \\=-2G[1-\frac{1}{2}]^{-1}\\ \\=\frac{-2G}{1-\frac{1}{2}}\\ \\ =-\frac{2G}{(\frac{1}{2})}\\ \\=-4G$

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