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  •  An object of mass  is supported by a massless string wound around a uniform cir

 An object of mass 1 \mathrm{~kg} is supported by a massless string wound around a uniform circular disc of mass ' 2 \mathrm{~kg} ' and radius ' 1 \mathrm{~m} '. if the string does not slip on the cylinder, find the velocity of the object at t=\1 \mathrm{s}. [Given, g=10 \mathrm{~m} / \mathrm{s}^2 ]

Option: 1

\frac{10}{3} m/s


Option: 2

5 m/s


Option: 3

\frac{5}{3} m/s


Option: 4

10m/s


Answers (1)

best_answer

\begin{gathered} m g-T=m a \\ TR =\frac{1}{2} M R^2 \alpha \\ T=\frac{1}{2} M a \\ m g-\frac{1}{2} M a=m a \end{gathered}

\begin{aligned} \left(\frac{1}{2} M+m\right) a & =m g \\ \left(\frac{1}{2} \times 2+1\right) a & =(1)(10) \\ 2 a & =10 \\ a & =5 \mathrm{~m} / \mathrm{s}^2 \end{aligned}

using,

        \begin{aligned} & v=u+a t \\ & v=0+(5)(1) \\ & v=5 \mathrm{~m} / \mathrm{s} \end{aligned}

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chirag

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