Question

In the figure shown neglecting friction andd mass of pulleys, what is the aacceleration of mass $B$?

• A. $\frac{g}{3}$
• B. $\frac{5g}{2}$
• C. $\frac{2g}{5}$
• D. $\frac{2g}{3}$

Answer 1

The correct option is C $\frac{2g}{5}$

Draw a free body diagram.

Find the value of acceleration.

For block $A$. Applying Newton's second law on section $A$

$mg-2T=m{a}_a\dots \left(i\right)$

For block $B$,

$T-mg=m{a}_b\dots \left(ii\right)$

and by constraint motion,

$-T\cdot a_b-2T\cdot a_a=0$

$a_b=-2a_a\dots \left(iii\right)$

$T-mg=-2m{a}_a\dots \left(iv\right)$

Solving $\left(i\right),$ and $\left(iv\right)$ get,

$a_a=-g/5\text{and}{a}_b=-2g/5$

Final Answer: $\frac{2g}{5}$