Two blocks of masses `m_(1) = 1 kg` and `m_(2) = 2 kg` are connected by a non-deformend light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. What minimum constant force F has to be applied in horizontal direction to the block of mass `m_(1)` in order to shift the other block? `(g = 10 m//s^(2))`

Options

A. `(m_(1)+m_(2)/(2))mug`
B. `(m_(2)+m_(1)/(2))mug`
C. `(m_(1)-m_(2)/(2))mug`
D. `(2m_(2)+m_(1)/(2))mug`

Answer

A

Explanation

Let force constant of spring is `k` then `mum_(2)g=kx` & `Fx-mum_(1)g-(1)/(2)kx^(2)=0`
`rArrF=(m_(1)+(m_(2))/(2))mug`