Q. 193.8( 16 Votes )

A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

Answer :

What we want to find is work done. We know that the work done to stop a moving body is the total kinetic energy of the body.


Work Done = KE = KErot + KEtran


Where KErot is rotational kinetic energy and


KEtran is translational kinetic energy


KErot = 1/2 Iω2


KEtran = 1/2 Mv2


Where M is mass of hoop


I is moment of inertia of hoop


v is velocity of centre of mass


ω is angular velocity


Now the given values are,


Mass of hoop, M = 100 Kg


Radius of hoop, R = 2 m


Speed of centre of mass of hoop, v = 20 Cm s-1


= .2 m s-1


The axis of rotation of hoop passes through point B, we know that velocity of point O (centre of loop) is v. If ω is angular velocity of hoop then,


v = R ω (R is Distance between axis and centre(O))



Where ω is angular velocity.


i.e. ω = v/R = 0.2/2 = .1 s-1


Moment of inertia of hoop, I = MR2


Where, M is mass of hoop


R is Radius of hoop


I = 100(2)2


I = 400 Kg m2


Total Kinetic Energy of hoop,


KE = KErot + KEtran


KErot = 1/2 400 × (.1)2


= 2 J


KEtran = 1/2 100 × (.2)2


= 2 J


Total Kinetic energy,


KE = 2 + 2 = 4 J


Work done to stop the moving hoop is equal to its KE which is 4 J


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Moment of Inertia | Some special casesMoment of Inertia | Some special casesMoment of Inertia | Some special cases40 mins
Interactive Quiz on Moment of InertiaInteractive Quiz on Moment of InertiaInteractive Quiz on Moment of Inertia56 mins
Important Questions on TorqueImportant Questions on TorqueImportant Questions on Torque43 mins
Centre of Mass Frame (C-Frame)Centre of Mass Frame (C-Frame)Centre of Mass Frame (C-Frame)59 mins
Angular momentum & its conservation | Getting Exam ReadyAngular momentum & its conservation | Getting Exam ReadyAngular momentum & its conservation | Getting Exam Ready37 mins
Understand Parallel & Perpendicular Axis Theorem in detailUnderstand Parallel & Perpendicular Axis Theorem in detailUnderstand Parallel & Perpendicular Axis Theorem in detail40 mins
Questions based on rotational motionQuestions based on rotational motionQuestions based on rotational motion44 mins
Kinematics of rotational motion about a fixed axisKinematics of rotational motion about a fixed axisKinematics of rotational motion about a fixed axis48 mins
Interactive Quiz on Torque and angular momentumInteractive Quiz on Torque and angular momentumInteractive Quiz on Torque and angular momentum48 mins
Motion of centre of mass {Theory}Motion of centre of mass {Theory}Motion of centre of mass {Theory}38 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :