A) \[2.5\,\,m\]
B) \[5\,\,m\]
C) \[7.5\,\,m\]
D) \[10\,\,m\]
Correct Answer: D
Solution :
Here: Mass of the cylinder \[m=10\,\,kg\] Initial velocity of cylinder\[v=10m/s\] Coefficient of friction between surface and the cylinder\[\mu =0.5\] The kinetic energy of the cylinder is \[=\frac{1}{2}m{{v}^{2}}\] \[=\frac{1}{2}\times 10\times {{10}^{2}}\] \[=500\,\,kg\,\,m/\sec \] ... (1) The work done by the cylinder in rolling over the plane is = Force of friction \[\times \] distance \[=\mu mg\times s\] \[=0.5\times 10\times 10\times s\] \[=50s\] ... (2) As the kinetic energy of the cylinder will be consumed in doing the work. Hence, from (1) and (2) \[500=50s\] \[s=\frac{500}{50}=10m\]
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