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)

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Answer:

Correct Answer: 34. (a)

Solution:

  1. (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}} $