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  • A rope is wrapped around the rim of a wheel of moment of inertia 0.10 Kg-m2 and radius  10 cm. The wheel is fixed such that it can freely rotate about its axis. If a person is pulli

A rope is wrapped around the rim of a wheel of moment of inertia 0.10 Kg-m2 and radius  10 cm. The wheel is fixed such that it can freely rotate about its axis. If a person is pulling the rope with the constant force of 10 N. Find the length of the rope detached from the pulley for t=0 to t=10 s

Option: 1

25 m


Option: 2

50 m


Option: 3

75 m


Option: 4

100 m


Answers (1)

best_answer

\tau=I \alpha \\

\alpha=\frac{\tau}{I}=\frac{r F}{I} \\

\alpha=\frac{0.1 \times 10}{0.1}=10 \,\mathrm{rad} / \mathrm{s}^2 \\

a_t=r \alpha=0.1 \times 10=1 \mathrm{~m} / \mathrm{s}^2 .

Assuming the length of the rope freed is ' s '

 S=u t+\frac{1}{2} a t^2 \\
S=0+\frac{1}{2} \times 1 \times 100 \\

S=50 \mathrm{~m}

Posted by

sudhir.kumar

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