A thin and uniform rod of mass $M$ and length $L$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement($s$) is/are correct, when the rod makes an angle $60^{\circ}$ with vertical ? [ $g$ is the acceleration due to gravity]
$(1)$ The radial acceleration of the rod's center of mass will be $\frac{3 g }{4}$
$(2)$ The angular acceleration of the rod will be $\frac{2 g }{ L }$
$(3)$ The angular speed of the rod will be $\sqrt{\frac{3 g}{2 L}}$
$(4)$ The normal reaction force from the floor on the rod will be $\frac{ Mg }{16}$
A thin and uniform rod of mass $M$ and length $L$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement($s$) is/are correct, when the rod makes an angle $60^{\circ}$ with vertical ? [ $g$ is the acceleration due to gravity]
$(1)$ The radial acceleration of the rod's center of mass will be $\frac{3 g }{4}$
$(2)$ The angular acceleration of the rod will be $\frac{2 g }{ L }$
$(3)$ The angular speed of the rod will be $\sqrt{\frac{3 g}{2 L}}$
$(4)$ The normal reaction force from the floor on the rod will be $\frac{ Mg }{16}$
- [IIT 2019]
- A
$1,2,3$
- B
$1,2,4$
- C
$1,3,4$
- D
$1,2$
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