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Page # 86
Sol.
ROTATIONAL DYNAMICS
33. A uniform circular disc of mass 50 kg and
radius 0.4 m is rotating with an angular velocity
of 10 rad s-1 about its own axis, which is vertical.
Two uniform circular rings, each of mass 6.25 kg
and radius 0.2 m, are gently placed symmetrically
on the disc in such a manner that they are
touching each other along the axis of the disc
and are horizontal. Assume that the friction is
large enough such that the rings are at rest
relative to the disc and the system rotates about
the original axis. The new angular velocity (in rad
s-1) of the system is :
[JEE 2013]
Sol.
32. 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.
(B) Cylinder P has larger linear acceleration than
cylinder Q.
(C) Both cylinders reach the ground with same
translational kinetic energy.
(D) Cylinder Q reaches the ground with larger
angular speed.
[JEE 2012]
Sol.
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