Mass $m$ is divided into two parts $X m$ and $(1 - X) m$ . For a given separation, the value of $X$ for which the gravitational force of attraction between the two pieces becomes maximum is :

\frac{1}{2}

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\frac{3}{5}

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1

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Solution

The correct option is A $\frac{1}{2}$
Force exerted by the bodies is given by $F = \frac{G m m X (1 - X)}{R^{2}}$
For maximum force , $X (1 - X)$ should be maximum.
Differentiating $X (1 - X)$ gives $1 - 2 * X = 0$ or $X = \frac{1}{2}$

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Mass m is divided into two parts X m and (1−X) m. For a given separation, the value of X for which the gravitational force of attraction between the two pieces becomes maximum is :

The correct option is A 12Force exerted by the bodies is given by F=GmmX(1−X)R2For maximum force , X(1−X) should be maximum.Differentiating X(1−X) gives 1−2∗X=0 or X=12

Mass $m$ is divided into two parts $X m$ and $(1 - X) m$ . For a given separation, the value of $X$ for which the gravitational force of attraction between the two pieces becomes maximum is :

The correct option is A $\frac{1}{2}$
Force exerted by the bodies is given by $F = \frac{G m m X (1 - X)}{R^{2}}$
For maximum force , $X (1 - X)$ should be maximum.
Differentiating $X (1 - X)$ gives $1 - 2 * X = 0$ or $X = \frac{1}{2}$