Q)A block of mass m is attached with a massless spring of force constant k.The block is placed over a rough inclined surface for which coefficient of friction is ¾.Find the minimum value of M required to movethe block up the plane.(neglect friction in pulley.neglect mass of string and pulley).See the figure in the attachment.plz solve and explain sir.

This can be solved in a better and quicker method using work. Let spring be displaced by a distance x. So M moves by a distance x too. 1/2kx^2=Mgx......equation 1Now as block moves up friction is applied downwards and kx up the plane, Kx=mgsin(theta)+3/4mgcos(theta)Kx=6mg/5Replacing this in equation 1We have M=3m/5

f+mgsin(theta)=tensionf=friction ....f=3/4mgcos(theta)tension=Mgequate it and yu will get the answer