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Two sphere of masses m and M are situate...

Two sphere of masses `m` and `M` are situated in air and the gravitational force between them is `F`. The space around the masses in now filled with a liquid of specific gravity `3`. The gravitational force will now be

A

`F/9`

B

`3F`

C

`F`

D

`F/3`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze how the gravitational force between two masses is affected by the medium surrounding them. ### Step-by-Step Solution: 1. **Understanding Gravitational Force**: The gravitational force \( F \) between two masses \( m \) and \( M \) separated by a distance \( r \) in a vacuum or air is given by Newton's law of gravitation: \[ F = \frac{G \cdot m \cdot M}{r^2} \] where \( G \) is the gravitational constant. 2. **Effect of Medium**: The problem states that the space around the masses is filled with a liquid of specific gravity 3. Specific gravity is a measure of the density of a substance compared to the density of water. Since the specific gravity of the liquid is 3, its density \( \rho \) can be expressed as: \[ \rho = 3 \cdot \rho_{\text{water}} = 3 \cdot 1000 \, \text{kg/m}^3 = 3000 \, \text{kg/m}^3 \] However, it is important to note that the gravitational force between two masses does not depend on the medium in which they are placed. 3. **Conclusion**: Since the gravitational force is independent of the surrounding medium (whether it is air, liquid, or solid), the gravitational force \( F \) between the two spheres will remain the same even when the space around them is filled with the liquid. Therefore, the gravitational force will still be: \[ F = \frac{G \cdot m \cdot M}{r^2} \] ### Final Answer: The gravitational force will remain \( F \).

To solve the problem, we need to analyze how the gravitational force between two masses is affected by the medium surrounding them. ### Step-by-Step Solution: 1. **Understanding Gravitational Force**: The gravitational force \( F \) between two masses \( m \) and \( M \) separated by a distance \( r \) in a vacuum or air is given by Newton's law of gravitation: \[ F = \frac{G \cdot m \cdot M}{r^2} ...
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