A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$, the initial angular acceleration of the rod will be
A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$, the initial angular acceleration of the rod will be
- [AIPMT 2006]
- [AIPMT 2007]
- A
$\frac{{mgl}}{2}$
- B
$\frac{3}{2}gl$
- C
$\;\frac{{3g}}{{2l}}$
- D
$\;\frac{{2g}}{{3l}}$
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$(B)$ The horizontal component of reaction force at $O$ is equal to $W$ for $\alpha=0.5$
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One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$, at a height $L$ above the hinge at point $O$. A block of weight $\alpha W$ is attached at the point $P$ of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of $(2 \sqrt{2}) W$. Which of the following statement($s$) is(are) correct ?
$(A)$ The vertical component of reaction force at $O$ does not depend on $\alpha$
$(B)$ The horizontal component of reaction force at $O$ is equal to $W$ for $\alpha=0.5$
$(C)$ The tension in the rope is $2 W$ for $\alpha=0.5$
$(D)$ The rope breaks if $\alpha>1.5$
- [IIT 2021]