A) 10 m
B) 7.5 m
C) 5 m
D) 2.5 m
Correct Answer: A
Solution :
Key Idea: Kinetic energy of cylinder is consumed in doing work against friction in rolling motion. A body of mass \[m\] moving with velocity\[v\], Possess kinetic energy given by \[K=\frac{1}{2}m{{v}^{2}}\] ?..(1) This kinetic energy is utilized in doing work against the frictional forces. \[W=\mu mgs\] ?(2) Where \[\mu \] is coefficient of kinetic friction, \[m\] is mass, \[g\] is gravity and \[s\] is displacement. Equating Egs. (1) and (2), we get \[\frac{1}{2}m{{v}^{2}}=\mu mgs\] Where\[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}\times 10\times {{\left( 10 \right)}^{2}}=500\,\,kg-m/s\] Given, \[v=10\,\,m/s,\,\,\mu =0.5,\,m=10\,kg\], \[g=10\,m/{{s}^{2}}\] \[\Rightarrow \] \[s=\frac{\frac{1}{2}\times m\times {{\left( 10 \right)}^{2}}}{\mu mg}\] \[=\frac{50}{0.5\times 10}=10\,m.\]
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