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  4. A man pushes a cylindrical drum through a board of length l as shown in figure-5.109. The drum rolls forward on the ground a distance of (l/2). There is no slipping at any instant. During the process of pushing the board the distance moved by the man on the ground is :

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Q. A man pushes a cylindrical drum through a board of length $l$ as shown in figure-5.109. The drum rolls forward on the ground a distance of $\frac{l}{2}$. There is no slipping at any instant. During the process of pushing the board the distance moved by the man on the ground is :Physics Question Image

System of Particles and Rotational Motion

Solution:

Let speed of $COM$ of cylindrical drum is $v$, then time taken by it to cover a distance of $\frac{l}{2}$
$t=\frac{l}{2 v}\,\,\,\, ...(1)$
Speed of plank $=2 v$
[due to pure rolling of drum]
Distance travelled by plank is
$s=2 v \times t $
$\Rightarrow s=2 v \times \frac{l}{2 v} $
$\Rightarrow s=l$