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TS EAMCET · Physics · Gravitation

Infinite number of spheres, each of mass \(m\) are placed on the \(X\)-axis at distances \(1,2,4,8\), 16 ...... metres from origin. The magnitude of the gravitational field at the origin is

  1. A \(\frac{2}{3} \mathrm{Gm}\)
  2. B \(\frac{4}{3} \mathrm{Gm}\)
  3. C \(\mathrm{Gm}\)
  4. D \(6 \mathrm{Gm}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{4}{3} \mathrm{Gm}\)

Step-by-step Solution

Detailed explanation

Gravitational field at the origin due to mass at 1,2 , \(4,8,16 \ldots\) \( \begin{aligned} & =\frac{G m}{(1)^2}+\frac{G m}{(2)^2}+\frac{G m}{(4)^2}+\frac{G m}{(8)^2} \ldots . . \\ & =G m\left[1+\frac{1}{4}+\frac{1}{16}+\ldots \ldots\right]=\frac{4 G m}{3} \end{aligned} \)
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