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  4. A Uniform rod AB is hinged at its end A and the other end of the rod is connected to a block through a massless string as shown in the figure. The pulley is smooth and massless. Masses of the block and the rod are same and are equal to m . The acceleration of the block just after the release from this position is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-2hjmqeu4huusjavr.jpg />

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Q. A Uniform rod $AB$ is hinged at its end $A$ and the other end of the rod is connected to a block through a massless string as shown in the figure. The pulley is smooth and massless. Masses of the block and the rod are same and are equal to $m$ . The acceleration of the block just after the release from this position is
Question

NTA AbhyasNTA Abhyas 2022

Solution:

For the rod: $\text{T}\ell -\text{mg}\left(\frac{\ell }{2}\right)=\frac{\text{m} \ell ^{2}}{3}\times \frac{\text{a}}{\ell }$ ...(i)
For the: $mg-T=ma$ ...(ii)
Solving (i) and (ii) we get: $a=\frac{3 g}{8}$

Solution