Question

Find out the acceleration of the block $B$ in the given systems:

Answer 1

$a)2mg-2T=2m(a/2)mg-T=\frac{ma}{2}\to (1)$

At B

$T=ma\to \left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$

$mg=\frac{3ma}{2}a=\frac{2g}{3}$

$\left(b\right)$ For A

$3mg-3T=3m\left(a/3\right)mg-T=\frac{ma}{3}\to \left(1\right)$

For B

$T=ma\to \left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$

$mg=\frac{4ma}{3}a=\frac{3g}{4}$