Two identical ladders, each of mass M and length L are resting on the rough horizontal surface as shown in the figure. A block of mass m hangs from P. if the system is in equilibrium, find the magnitude and the direction of frictional force at A and B.

Answer

A, B, C

Explanation

The various forces acting on the ladders are shown in the
figure.
Sicce the system is in equilibrium, therefore
`SimgaF_y = 0`
`rArr Mg + mg+Mg = N+N

`rArr N = ((2M+m)g)/(2) ….(i)`
`rArr mgxx(L)/(2)cos theta + fxxLsin theta = NL cos theta `
`rArr f = (NL cos theta - (Mgl)/(2) cos theta)/(L sin theta)= N cot theta - (Mg)/(2) cot theta`
`rArr f = [(2N+m)/(2))g - (Mg)/(2)]cos theta`
`rArr f= [(M + m) (g)/(2)] cot theta`