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

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

1. A

2J

2. B

1J

3. C

3J

4. D

30 kJ

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### Solution:

Work required = change in kinetic energy

Final KE = 0
Initial $\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^{2}+\frac{1}{2}{\mathrm{l\omega }}^{2}=\frac{1}{2}{\mathrm{mv}}^{2}+\frac{1}{2}{\mathrm{mv}}^{2}\left(\frac{{\mathrm{K}}^{2}}{{\mathrm{R}}^{2}}\right)=\frac{3}{4}{\mathrm{mv}}^{2}$

$\left|∆\mathrm{KE}\right|=3\mathrm{J}$

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