Laws of Motion - Result Question 34
34. Two blocks $m_1=5 gm$ and $m_2=10 gm$ are hung vertically over a light frictionless pulley as shown here. What is the acceleration of the masses when they are left free?
[2000]
(a) $g / 3$
(b) $g / 2$
(c) $g$
(d) $g / 5$
(where $g$ is acceleration due to gravity)
Show Answer
Answer:
Correct Answer: 34. (a)
Solution:
- (a) Let $T$ be the tension in the string.
$ \begin{equation*} \therefore 10 g-T=10 a \tag{i} \end{equation*} $
$ \begin{equation*} T-5 g=5 a \tag{ii} \end{equation*} $
Adding (i) and (ii),
$ 5 g=15 a \Rightarrow a=\frac{g}{3} m / s^{2} $
Whe pulley have a finite mass $m$ then acceleration,
$ a=\frac{m_1-m_2}{m_1+m_2+\frac{m}{2}} $
