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
- A \(\frac{2}{3} \mathrm{Gm}\)
- B \(\frac{4}{3} \mathrm{Gm}\)
- C \(\mathrm{Gm}\)
- D \(6 \mathrm{Gm}\)
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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