In the given arrangement, the mass m of the block, M of the wedge and 'x', the angle of the wedge are known. Friction is absent and the pulleys and threads are massless. Find the acceleration of the wedge.

 Sorry for not being able to post the picture of the arrangement........................

Since string is of constant length, hence distance travelled by bigger wedge is same as distance travelled by smaller mass along the surface.

Hence magnitude of acceleration of M is same as the magnitude of accn. of m along the surface.

w1= acceleration of m w.r.t. ground

w12= acceleration of m w.r.t. M (along surface)

w2= acceleration of M

Vector w1= Vector sum of w12 and w2

Since magnitude of w12 , and w2 is same(say w)

w1=

== w  .....................(1)

mgSin-T=m(w -wCos) ..........................................................(2)

T-Tcos+NSin=Mw....................................................................(3)

mgcos-N=mwSin.........................................................................(4)

Solve above equations for w

w=mgSin/[M+2m(1-cos)]