Two masses $m_1=1\text{ kg}$ and $m_2=3\text{ kg}$ are connected by a string over a frictionless pulley. What is the acceleration $a$ of the system in ${\text{m/s}}^2$? (Take $g=10{\text{ m/s}}^2$)

Solution

1. The acceleration formula is $a=\frac{(m_2-m_1)g}{m_1+m_2}$.
2. Substitute the values: $a=\frac{(3-1)\times 10}{3+1}$.
3. Simplify the expression: $$\begin{array}{rl}a& =\frac{2\times 10}{4}\\ & =\frac{20}{4}\end{array}$$.
4. Calculate the result: $a=5{\text{ m/s}}^2$.
5. Hence the answer is (B).