Rotation 3 Question 20

26. Two identical uniform discs roll without slipping on two different surfaces AB and CD (see figure) starting at A and C with linear speeds v1 and v2, respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and v1=3m/s, then v2 in m/s is (g=10m/s2)

(2015 Adv.)

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Answer:

Correct Answer: 26. 7

Solution:

  1. In case of pure rolling, mechanical energy remains constant (as work-done by friction is zero). Further in case of a disc,

 translational kinetic energy  rotational kinetic energy =KTKR=12mv212Iω2

=mv212mR2v2R=21

or,

KT=23( Total kinetic energy )

or, Total kinetic energy

K=32KT=3212mv2=34mv2

Decrease in potential energy =increase in kinetic energy

or, mgh=34m(vf2vi2) or vf=43gh+vi2

As final velocity in both cases is same.

So, value of 43gh+vi2 should be same in both cases.

43×10×30+(3)2=43×10×27+(v2)2

Solving this equation, we get

v2=7m/s



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