Question

The magnitude of the gravitational force between a particle of mass $m_1$ and another particle of mass $m_2$ is $F=\frac{G{m}_1{m}_2}{x^2}$. The work required to increase the separation of the particles from $x=x_1$ to ($x_1$ + d) is

• A. $\frac{G{m}_1{m}_2{x}_1}{d(x_1+d)}$
• B. $\frac{G{m}_1{m}_{2}d}{x_1(x_1+d)}$
• C. $\frac{G{m}_1{m}_{2}x{{}_1}^2}{d(x_1+d)}$
• D. $\frac{G{m}_1{m}_2{d}^2}{x_1(x_1+d)}$

Answer 1

The correct option is B $\frac{G{m}_1{m}_{2}d}{x_1(x_1+d)}$

$F=\frac{G{m}_1{m}_2}{x^2}$

And work done, $W={\int }_{x_1}^{x_1+d}F=\frac{G{m}_1{m}_{2}d}{x_1(x_1+d)}$