Question

Two masses $2kg$ and $3kg$ are attached to the end of the string passed over a frictionless pulley fixed at the the top. The tension in the string and acceleration of the masses are

• A. $\frac{7g}{8},\frac{7g}{8}$
• B. $\frac{21g}{8},\frac{g}{8}$
• C. $\frac{12g}{8},\frac{g}{5}$
• D. $\frac{12g}{5},\frac{g}{5}$

Answer 1

The correct option is D $\frac{12g}{5},\frac{g}{5}$

Both the masses will have same acceleration being attached to the same string. Using the below two formulas for 2 mass system,
$T=\frac{2m_1{m}_2}{m_1+m_2}g=\frac{2\times 2\times 3}{2+3}g=\frac{12g}{5}$
$a=\left(\frac{m_2-m_1}{m_1+m_2}\right)g=\left(\frac{3-2}{2+3}\right)g=\frac{g}{5}$