Question

Neglect friction. Find accelerations of $m,2mand3m$ as shown in the figure. The wedge (inclination$={30}^o$) is fixed.

Answer 1

Refer to the fig. Attached with the solution

Here we can see that when block A moves a distance $x$ then it will free $x$ length of the string

So, acc. Of block A=acc. Of the string=acc. of block C=acc. of block B in vertical direction=$a$ (let's say)

Therefore acc. of block B in horizontal direction=$a$

Equilibrium eq. For block C

$mgsin\left(30°\right)-T=ma\to \left(equation1\right)$

Equilibrium eq. for block B in vertical direction

$T-2mg=2ma\to \left(equation2\right)$

Solving both equations we have $a=-g/2$