Question

A cylinder is rolling without slipping on a horizontal plank $P$. The friction between the plank $P$ and the cylinder is sufficient for no slipping. The coefficient of friction between the plank and the ground surface is zero. Initially, $P$ is attached with a string $S$ as shown in the figure. If the string is now burned, then

• A. Linear velocity of the cylinder will decrease and angular velocity will increase
• B. The plank will start motion with a speed $v$ along forward direction
• C. The plank will start motion with a speed $v$ along backward direction
• D. The plank will remain static

Answer 1

The correct option is D The plank will remain static

Draw a diagram of given problem


Calculate velocity of plank if string is burned

According to given question, initial friction between plank and cylinder is sufficient for no slipping,
Therefore,
$V_{CG}=V-R\omega$
It is given that, there is no slipping, hence
$V_{CG}=V_p$
$V-R\omega =V_p$
Again, we know that,
$\omega =V/R$
$V_P=V-\frac{RV}{R}=0$
The plank will remain static or fix.