Question

A disc of radius $2m$ and mass $100kg$ rolls on a horizontal floor. Its centre of mass has a speed of $20cm/s$. How much work is needed to stop it ?

• A. $3J$
• B. $30kJ$
• C. $2J$
• D. $1J$

Answer 1

The correct option is A $3J$

Given, $m=100kg,v=20cm/s,r=2m$
According to work-energy theorem,
The work done to stop the disc = Rotational K.E. + Translational K.E.
Rotational K.E. = $\frac{1}{2}I{\omega }^2$
( Here , $I=\frac{1}{2}m{r}^2\text{and}\omega =\frac{v}{r}$)
Substituting values, we get
Rotational KE = $1J$
Translational K.E. = $\frac{1}{2}m{v}^2$
Substituting values, we get
Translational K.E. = 2 $J$
So, total energy = $3J$ , which is the work needed to stop it .