1. Tardigrade
  2. Question
  3. Physics
  4. A carpet of mass M made of inextensile material is rolled along its length in the form of a cylinder of radius R and kept along a rough floor. The carpet starts unrolling without sliding on the floor, when a negligibly sniall push is given to it. The horizontal velocity of, the axis of a cylihderical part of the carpet when its radius is reduced to R/2 is

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Q. A carpet of mass M made of inextensile material is rolled along its length in the form of a cylinder of radius R and kept along a rough floor. The carpet starts unrolling without sliding on the floor, when a negligibly sniall push is given to it. The horizontal velocity of, the axis of a cylihderical part of the carpet when its radius is reduced to R/2 is

Solution:

Gain in KE = loss in PE
$\frac{1}{2} mV^2 \left[ 1 + \frac{K^2}{R^2} \right] = Mgh_2 - mgh_1$
where M = mass of carpet of radius R
m = mass of carpet of radius $\frac{R}{2}$
$_2 \alpha \, R $ and $h_1 \alpha \frac{R}{2}$ and also $m \alpha \left( \frac{R}{2} \right)^2$