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23 Feb 2012 00:01:29 IST

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Rotational mechanics Rolling question

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question - solid sphere,ring,disc having same mass and radius are placed at the top of an incline and released. the friction coefficient bw the objects and the incline are same but not sufficient to allow pure rolling .least time will be taken by-

a)solid sphere,b)the ring c)the disc d)all will take same time

also the smallest kinetic energy wil be acquired by-

A) ring b)sphere c)disc d)all achieve the same kinetic energy

ans - 1st question - (d) 2nd question-(A) , please explain ????

Comments (2)

Arjun Virmani

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Joined: 1 Jun 2009

Posts: 1330

25 Feb 2012 01:21:23 IST

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The time depends only on force exerted on the body.

as to find time we only req. linear acceleration and distance.

and the main force and the frictional force exerted on the bodies are same.

for Energy we have 1/2 mv² + 1/2 Iw²

so we'll have to see both.

1/2 mv² is same for all as m and linear v is same.

but let come to 1/2 Iw²

as the frictional force is same on all and the radius is same thrfr,

Angular torque is same, thrfr, angular momentum is same.i.e. Iw is same...

as Iw is same and I for ring > I for disc > I for sphere

thrfr w for ring < w for disc <w for sphere.

and thrfr the K.E.

SAHIL AAPAN

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Joined: 22 Feb 2012

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25 Feb 2012 22:38:53 IST

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thank you but why cant we think this way,since all stuff identical work done by frictional force is same ,

Wext= change in kinetic + change in potential enrgy

since work done by friction is same and change in potential energy is same , so change in kinetic energy must be same????? hence all should come down with same k.e????

please explain

thank you

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