A cord is wound round the circumference of a | vedclass

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

Question

(B) According to the law of conservation of energy,the potential energy lost by the falling weight is converted into the kinetic energy of the system

Vedclass · Accepted Answer

$\sqrt{\frac{2mgh}{I + mr^2}}$

Vedclass · Answer

(B) According to the law of conservation of energy,the potential energy lost by the falling weight is converted into the kinetic energy of the system (rotational kinetic energy of the wheel and translational kinetic energy of the weight).$mgh = \frac{1}{2}I\omega^2 + \frac{1}{2}mv^2$Since the cord is wound around the wheel,the linear velocity $v$ of the weight is related to the angular velocity $\omega$ of the wheel by $v = r\omega$.Substituting $v = r\omega$ into the energy equation:$mgh = \frac{1}{2}I\omega^2 + \frac{1}{2}m(r\omega)^2$$mgh = \frac{1}{2}(I + mr^2)\omega^2$Solving for $\omega$:$\omega^2 = \frac{2mgh}{I + mr^2}$$\omega = \sqrt{\frac{2mgh}{I + mr^2}}$

$A$ cord is wound round the circumference of a wheel of radius $r$. The axis of the wheel is horizontal and the moment of inertia about it is $I$. $A$ weight $mg$ is attached to the end of the cord and falls from rest. After falling through a distance $h$,the angular velocity of the wheel will be

Similar Questions

$A$ wheel is rotating at $1200 \ rpm$ and is slowed down at a rate of $4 \ rad/s^2$. The number of revolutions it completes before coming to rest is:

$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, then with what acceleration will the mass be released? (Assume $g =$ acceleration due to gravity)

$A$ straight rod of length $L$ is released on a frictionless horizontal floor in a vertical position. As it falls and slips,the distance of a point on the rod from the lower end,which follows a quarter circular locus,is

For a rigid body in rotational motion,if a particle at a distance of $5 \, cm$ from the axis of rotation has an angular velocity of $10 \, rad/s$,what is the linear velocity of a particle at a distance of $10 \, cm$ from the axis of rotation (in $, cm/s$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module