Consider the situation shown in the figure. Uniform rod of length $L$ can rotate freely about the hinge $A$ in vertical plane. Pulleys and string are light and frictionless. If therod remains horizontal at rest when the system is released then the mass of the rod is :
Consider the situation shown in the figure. Uniform rod of length $L$ can rotate freely about the hinge $A$ in vertical plane. Pulleys and string are light and frictionless. If therod remains horizontal at rest when the system is released then the mass of the rod is :
- A
$\frac{4}{3} M$
- B
$\frac{8}{3} M$
- C
$\frac{16}{3} M$
- D
$\frac{32}{3} M$
Similar Questions
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 $\alpha>1.5$
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]
Write the conditions for equilibrium of a rigid body.
Write the conditions for equilibrium of a rigid body.
$A$ thin rod of length $L$ is placed vertically on a frictionless horizontal floor and released with a negligible push to allow it to fall. At any moment, the rod makes an angle $\theta$ with the vertical. If the center of mass has acceleration $= A$, and the rod an angular acceleration $= \alpha$ at initial moment, then
$A$ thin rod of length $L$ is placed vertically on a frictionless horizontal floor and released with a negligible push to allow it to fall. At any moment, the rod makes an angle $\theta$ with the vertical. If the center of mass has acceleration $= A$, and the rod an angular acceleration $= \alpha$ at initial moment, then
As shown in Figure the two sides of a step ladder $BA$ and $CA$ are $1.6 m$ long and hinged at $A$. A rope $DE, 0.5 \;m$ is tied half way up. A weight $40\;kg$ is suspended from a point $F , 1.2\; m$ from $B$ along the ladder $BA$. Assuming the floor to be frictionless and neglecting the wetght of the ladder. find the tension in the rope and forces exerted by the floor on the ladder. (Take $g=9.8 \;m / s ^{2}$ )
As shown in Figure the two sides of a step ladder $BA$ and $CA$ are $1.6 m$ long and hinged at $A$. A rope $DE, 0.5 \;m$ is tied half way up. A weight $40\;kg$ is suspended from a point $F , 1.2\; m$ from $B$ along the ladder $BA$. Assuming the floor to be frictionless and neglecting the wetght of the ladder. find the tension in the rope and forces exerted by the floor on the ladder. (Take $g=9.8 \;m / s ^{2}$ )
A small $100$ $g$ sleeve $B$ can slide on a smooth, circular and rigid wire frame $A$ of radius $5$ $m$ placed in vertical place. The wire frame is rotating about its vertical diameter at $2$ $rad/s$. When the sleeve is brought at a particular angular position other than the bottom and the top of the ring, the sleeve will not slide on the wire frame. ......... $N$ is force of interaction between the sleeve and the wire frame at this position.
A small $100$ $g$ sleeve $B$ can slide on a smooth, circular and rigid wire frame $A$ of radius $5$ $m$ placed in vertical place. The wire frame is rotating about its vertical diameter at $2$ $rad/s$. When the sleeve is brought at a particular angular position other than the bottom and the top of the ring, the sleeve will not slide on the wire frame. ......... $N$ is force of interaction between the sleeve and the wire frame at this position.