First slide

Work

Question

Two blocks each of mass ‘m are placed on smooth horizontal surface. They attract each other with a force $F= - \frac{k}{r}$ , r is separation between the blocks. The work required to increase the separation between the blocks slowly from a to 4a is $k \ln 2 x,$ where $x$ is ______

Moderate

Solution

$\begin{array}{l} w = \int \vec{F} \cdot \vec{dr} = \int_{a}^{4 a} \frac{k}{r} dr \\ w = k [\ln r]_{a}^{4 a} = k [\ln 4 a - \ln a] \\ w = kln (\frac{4 a}{a}) = kln (2 \times 2) \\ ∴ x = 2 \end{array}$

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