Home
Class 11
PHYSICS
A hoop of radius 2m weights 100 kg. It r...

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

Text Solution

Verified by Experts

Moment of inertia of hoop about its center
`I = MR^(2)`
and energy of loop = translational kinetic energy of CM and rotational kinetic energy about axis through CM.
`= (1)/(2) mv^(2)._(CM) + (1)/(2) I omega^(2)" "[I = mR^(2) and omega = (v)/(R)]`
`= (1)/(2) mv^(2)._(CM) + (1)/(2) mR^(2) xx (v^(2)._(CM))/(R^(2)) = mv^(2)._(CM)`
Work done is stopping the hoop
= total KE of hoop `= mv^(2)._(CM) = 100 xx (0.2)^(2) = 4J`
Promotional Banner

Topper's Solved these Questions

  • MOTION OF SYSTEM OF PARTICLES AND RIGID BODIES

    SURA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS :|61 Videos

  • MOTION OF SYSTEM OF PARTICLES AND RIGID BODIES

    SURA PUBLICATION|Exercise MATCH THE FOLLOWING :|4 Videos

  • MOTION OF SYSTEM OF PARTICLES AND RIGID BODIES

    SURA PUBLICATION|Exercise CONCEPTUAL QUESTIONS|8 Videos

  • KINETIC THEORY OF GASES

    SURA PUBLICATION|Exercise VALUE BASED QUESTIONS|4 Videos

  • NATURE OF PHYSICAL WORLD AND MEASUREMENT

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS|241 Videos

Similar Questions

Explore conceptually related problems

A uniform sphere of mass 200 g rolls without slipping on a plane surface so that its centre moves at a speed of 2.00 cm/s. Find its kinetic energy.

A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be (Take g = 10m/ s^2 ).

A box is pushed through a distance of 4m across a floor offering 100N resistance. How much work is done by the resisting force ?

A cycle together with its rider weighs 100 kg. How much work is needed to set it moving at 3 m/s (AS_(1))

A block of mass 30.0 kg is being brought down by a chain. If the block acquires as speed of 40.0 (cm)/s in dropping down 2.00 m ,find the work done by the chain during the process.

A ball, intially at the top of the inclined hill, is allowed to roll down. At the bottom its speed is 4 m/s. Next the ball is again rolled down the hill, but this time it does not start from rest. It has an initial speed of 3 m/s. How fast is it going when it gets to the bottom ?

A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the centre and stops after the collision. Find a. the velocity of the cente of the rod and b. the angular velocity of the rod abut its centre just after the collision.

A diver having a moment of inertia of 6.0 kg-m^2 about an axis through its centre of mass rotates at an angular speed of 2 rad/s about this axis. If he folds his hands and feet to decrease the moment of inertia to 5.0 kg-m^2 what will be the new angular speed?

A uniform rod of mass m and length l is struck at an end by a force F perpendicular to the rod for a short time interval t. Calculate a. the speed of the centre of mass ,b. the angular speed of the rod about centre of mass, c. the kinetic energy of the rod and d. the angular moment of the rod about the centre of mass after the force has stopped to act. Assume that t is so small that the rod does not apreciably change its direction while the force acts.

A mat of mass 1kg and length 1m is placed on the floor. One end of the mat is pulled with a constant speed of 1m/s towards the other end till the other end comes in to motion (till the mat is reverse). How much force is required to do this ?