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Question

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is (are) correct ?

A
Both cylinders P and Q reach the ground at the same time.
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B
Cylinder P has larger linear acceleration than cylinder Q.
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C
Both cylinders reach the ground with same translational kinetic energy
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D
Cylinder Q reaches the ground with larger angular speed
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Solution

The correct option is D Cylinder Q reaches the ground with larger angular speed

Translational motion :
mgsinθf=macm...........(i)
Rotational motion fR=Icmα..........(ii)
Rolling without slipping αR=acm........(iii)
From (ii) & (iii) f=IcmacmR2
Put this in (i)
mgsinθIcmacmR2=macm
acm=mgsinθ(IcmR2+m)
As IP>IQ
So aP<aQ
So, Vcm(Q)>vcm(P)
Hence ωQ>ωP

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