Question

Two blocks each of mass m are placed on a smooth horizontal surface. they attract each other with a force
F=k/r, where r is the separation between them. Calculate work required to increase the separation between the blocks slowly from a to 2a​

Answer 1

Answer:

$\boxed{\mathfrak{Work \ required \ to \ increase \ seperation \ (W) = k \ log2}}$

Explanation:

Force of attraction between the blocks:

$\rm F = \dfrac{k}{r}$

r → Seperation between the blocks

k → Constant

Work done by a variable force is given as:

$\boxed{ \bold{W = \int\limits^{x_2}_{x_1} F(x).dx}}$

For increasing seperation between blocks from $\sf x_1 = a$ to $\sf x_2 = 2a$ work required is:

$\rm \implies W = \int\limits^{2a}_{a} \dfrac{k}{x} .dx \\ \\ \rm \implies W = k \: logx \Big|_{a}^{2a} \\ \\ \rm \implies W = k \: (log \: 2a - log \: a) \\ \\ \rm \implies W = k \: log \frac{2 \cancel{a}}{\cancel{a}} \\ \\ \rm \implies W = k \: log2 \:$

Answer 2

Explanation:

hey mate;

hope it will help you!!