A single wire ACB passes through a smooth rin | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $T$ be the tension in the wire. Since the ring is smooth,the tension is the same throughout the wire.Resolving the forces acting on the ring $

Vedclass · Accepted Answer

$\sqrt{rg}$

Vedclass · Answer

(A) Let $T$ be the tension in the wire. Since the ring is smooth,the tension is the same throughout the wire.Resolving the forces acting on the ring $C$ along the vertical ($y$-axis) and horizontal ($x$-axis) directions:Along the vertical direction,the sum of the vertical components of tension balances the weight of the ring:$T \cos 30^{\circ} + T \cos 60^{\circ} = mg$$T \left( \frac{\sqrt{3}}{2} + \frac{1}{2} \right) = mg$$T \left( \frac{\sqrt{3} + 1}{2} \right) = mg$ $...(i)$Along the horizontal direction,the sum of the horizontal components of tension provides the necessary centripetal force:$T \sin 30^{\circ} + T \sin 60^{\circ} = \frac{mv^2}{r}$$T \left( \frac{1}{2} + \frac{\sqrt{3}}{2} \right) = \frac{mv^2}{r}$$T \left( \frac{\sqrt{3} + 1}{2} \right) = \frac{mv^2}{r}$ $...(ii)$Dividing equation $(ii)$ by equation $(i)$:$\frac{T \left( \frac{\sqrt{3} + 1}{2} \right)}{T \left( \frac{\sqrt{3} + 1}{2} \right)} = \frac{mv^2/r}{mg}$$1 = \frac{v^2}{rg}$$v^2 = rg$$v = \sqrt{rg}$

$A$ single wire $ACB$ passes through a smooth ring at $C$ which revolves at a constant speed in a horizontal circle of radius $r$ as shown in the figure. The speed of revolution is

Similar Questions

$A$ car of mass $m$ is crossing a convex bridge of radius of curvature $R$ with speed $V$. At the highest point, the thrust (normal force) is ($g =$ gravitational acceleration).

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

$A$ stone of mass $16 \, kg$ is attached to a string $144 \, m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16 \, N$. The maximum velocity of revolution that can be given to the stone without breaking it will be ....... $m/s$.

$A$ particle of mass $m$ is moving in a circular path of radius $r$ in a plane. Its angular momentum is $L$. The value of the centripetal force acting on the particle is:

$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module