In figure shown, pulleys are ideal. Initially the system is in equilibrium and string connecting $$m2$$ to rigid support below is cut. What is the initial acceleration (in$$ $$m/s2) of $$m2$$? Given $$m1=9kg$$;$$m2=3kg$$

At equilibrium $$2T=m1g$$⇒$$T=45N$$ ......(i)T$$−$$m2g=T1$$ ......$$(ii) As string is at cut then $$T1=0T$$−$$m2g=m1a$$⇒$$45$$−$$30=3$$×$$aa=5m/s2$$

Application of Newtons laws

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Question

In figure shown, pulleys are ideal. Initially the system is in equilibrium and string connecting m₂ to rigid support below is cut. What is the initial acceleration (in m/s²) of m₂?
$(Given m_{1} = 9 kg; m_{2} = 3 kg)$

Moderate

Solution

$At equilibrium 2 T = m_{1} g \Rightarrow T = 45 N . . . . . . (i)$
$T - m_{2} g = T_{1} . . . . . . (i i)$
$As string is at cut then T_{1} = 0$
$\begin{array}{l} T - m_{2} g = m_{1} a \Rightarrow 45 - 30 = 3 \times a \\ a = 5 m / s^{2} \end{array}$

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