Question

Figure shows a pulley (disc) of mass $m$ and radius $r$ with the blocks of masses $m_1$ and $m_2$ attached with light and unstretched string. The angular acceleration $\left(\alpha \right)$ of the pulley is (Assume no slipping between the string and pulley,$m_1=4kg,m_2=6kg,m_2=kg,r=10cm$ and $g=10m/s^2$)

• A. $\frac{50}{11}rad/s^2$
• B. $\frac{100}{11}rad/s^2$
• C. $\frac{200}{11}rad/s^2$
• D. $20rad/s^2$

Answer 1

The correct option is D $20rad/s^2$

$6g-T=6a\text{(1)}$

$T-4g=4a\text{(2)}$

Adding (1) and (2)

$2g=10a\Rightarrow a=\frac{g}{5}$

The pulley will also rotate with the linear acceleration 'a'.

So , its angular acceleration$=\omega$

$=\frac{a}{r}=\frac{g}{5\times 10}\times 100$

$=\frac{1000}{50}=20rad{s}^{-2}$