A monkey pulls the midpoint of a `10 cm` long light inextensible string connecting two identical objects `A` and `B` lying on smooth table of masses `0.3 kg` continuously along the perpendicular objects of line joining the masses .The masses are found to apporoach each other at a relative acceleration of `5 m s^(-2)` when they are `6 cm` apart .The constant force applied by monkey is

Options

A. `4 N`
B. `2 N`
C. `3 N`
D. None of these

Answer

B

Explanation

Relative acceleration

`a_(r) = 2a`
`:. a = (a_(r))/(2) = 2.5 m//s^(2)`
At point `p`
`2 T cos theta = F`
`:. T = (F)/(2 cos theta)`
At mass `m`
component of `T` along the other mass `m` is `T sin theta`
`:. a = (T sin theta)/(m) = ((F)/(2 cos theta)) (( sin theta)/(m))`
`:. F = (2 ma)/(tan theta) = (2 xx 0.3 xx 2.5)/((3//4))`
`= 2 N`