The friction coeficient bettween the board and the floor shownin filgure is `mu`. Find the maximum force that the man can exert on the rope so tht the board does not slipon the floor.

Explanation

Let the minimum force exerted by the man is T
From the free body diagram, `
`R+T=Mg`
`rarr R=Mg-T`.i
Again R-R-mg-0`
`R_1=R+mg`..ii
`and T-muR_1=0`
From equatioon ii, `T-mu(r+mg)=0`
`rarr T-muR-mu mg=0`
`rarr T-mu(Mg-T)-mu mg =0`
`T-mu Mg+mut-mu mg =0`


`T(1+mu)=muMg+mumg`
`rarr T=(mu(M+m)g)/(1+mu)`
Maximum force exerted by man is `(mu(M+m)g)/(1+mu)`