A ring of mass m connected through a string of length L with a block of mass M. If the ring is moving up with acceleration a_(m) and a_(M) is the acceleration of block. The relation between a_(m) and a_(M) is.

A ring of mass m connected through a string of length L with a block o

1.	A ring of mass m connected through a string of length L with a block of mass M. If the ring is moving up with acceleration a_(m) and a_(M) is the acceleration of block. The relation between a_(m) and a_(M) is.
Answer» Solution :As the length of the srting is constant, `L = SQRT(d^(2)+y^(2))+x` Since, L is constant, differentiating with respect to time t, we get `(DL)/(dt)=(1)/(2)(2y)/((d^(2)+y^(2))^((1)/(2)))((DY)/(dt))+(DX)/(dt)=0` Since `(dy)/(dx)=v_(m)` and `(dx)/(dt)=v_(M)` and `cos theta = (y)/(sqrt(d^(2)+y^(2)))` so `v_(M)=-v_(m)cos theta` By differentiating, relation between `a_(m)` and `a_(M)` can be obtained, however, while doing so remember that `cos theta` is not constant, but it is variable. `a_(M)=-a_(m)cos theta`.