A bob of mass m is tied by a massless string | vedclass

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

Question

(A) Let the angular velocity of the disc be $\omega$ and the linear velocity of the bob be $v$. Since there is no slipping,$v = R\omega$.Applying the

Vedclass · Accepted Answer

$\frac{2}{R} \sqrt{\frac{gh}{3}}$

Vedclass · Answer

(A) Let the angular velocity of the disc be $\omega$ and the linear velocity of the bob be $v$. Since there is no slipping,$v = R\omega$.Applying the law of conservation of energy: The loss in potential energy of the bob equals the gain in kinetic energy of the bob plus the gain in rotational kinetic energy of the disc.$mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$For a disc,the moment of inertia $I = \frac{1}{2}mR^2$.Substituting $I$ and $v = R\omega$ into the equation:$mgh = \frac{1}{2}m(R\omega)^2 + \frac{1}{2}(\frac{1}{2}mR^2)\omega^2$$mgh = \frac{1}{2}mR^2\omega^2 + \frac{1}{4}mR^2\omega^2$$mgh = \frac{3}{4}mR^2\omega^2$$gh = \frac{3}{4}R^2\omega^2$$\omega^2 = \frac{4gh}{3R^2}$$\omega = \frac{2}{R} \sqrt{\frac{gh}{3}}$.

Similar Questions

$A$ block of mass $2\,kg$ hangs from the rim of a wheel of radius $0.5\,m$. On releasing from rest,the block falls through $5\,m$ height in $2\,s$. The moment of inertia of the wheel will be ...... $kg \cdot m^2$.

$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

$A$ uniform solid cylinder of mass $M$ and radius $R$ rotates about a frictionless horizontal axle. Two similar masses $m$ are suspended with the help of two ropes wrapped around the cylinder. If the system is released from rest,then the acceleration of each mass will be

Let $\vec{A}$ be a unit vector along the axis of rotation of a purely rotating body and $\vec{B}$ be a unit vector along the velocity of a particle $P$ of the body away from the axis. The value of $\vec{A} \cdot \vec{B}$ is

$A$ rigid rod of length $\ell$ is sliding. At some instant,the position of the rod is as shown in the figure. End $A$ has a constant velocity $v_0$ along the $x$-axis. At $t = 0$,the rod is vertical with end $B$ at $y = \ell$. Which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module