The gravitational force between two bodies of the same mass placed at a distance ‘d’ apart is 'X'. If the mass of both bodies is doubled, and the distance between them is reduced to d/4, what will be the new gravitational force in terms of X?
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A.
16X
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B.
X/64
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C.
64X
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D.
X/16
Correct Answer:
C. 64X
Explanation:
The gravitational force $F$ between two objects is determined by the formula $F = G \frac{m_1 m_2}{d^2}$. In the initial scenario, the force is $X = G \frac{m \cdot m}{d^2} = G \frac{m^2}{d^2}$. If the mass of both bodies is doubled ($2m$) and the distance is reduced to one-fourth ($d/4$), the new force $F'$ is calculated as $G \frac{(2m)(2m)}{(d/4)^2}$. This simplifies to $G \frac{4m^2}{d^2/16}$, which further simplifies to $16 \cdot 4 \cdot G \frac{m^2}{d^2} = 64 \cdot (G \frac{m^2}{d^2})$. Since the original force $X$ is $G \frac{m^2}{d^2}$, the new gravitational force is $64X$.
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