The red carpets unrolls, show time
A
\color \red{red~carpet}
of mass
made of inextensible material is rolled along its length in the form of a
of Radius
and is kept on a
rough floor
. The carpet starts unrolling
without sliding
on the floor when a negligibly small push is given to it.The
of the axis of the
cylindrical part of the carpet
when its radius reduces to
is
where are and is acceleration due to gravity
Find
for more cool problems refer my set
The answer is 17.
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It could be easily solved by using conservation of energy. U i + K i = U f + K I Note that the portion of the carpet that went flat will have no contribution to final potential energy if we take ground as reference line. Also mass of the new cylinder will be 4 m m g R = 4 m g 2 R + 2 1 4 m v 2 + 2 1 I ω 2 Did you observe that this is the case of pure rolling so , we can say v = 2 R ω And also by the basics of rotational motion we know that Moment of Inertia of a cylinder is 2 M h 2 about its axis passing through center if the circular faces. So here it is 2 m ( 2 R ) 2 Plugging in the values and doing some more calculations will take you to v = 3 1 4 g R