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  • A massless thread is tightly wound over a uniform hollow cylinder of radius ' 

A massless thread is tightly wound over a uniform hollow cylinder of radius ' 10 \mathrm{~cm} '. This cylinder is placed on a smooth surface and thread is being palled with the constant force of '10 \mathrm{~N}'. If the cylinder was initially at rest, find its Kinetic energy when '550 \mathrm{~cm}' length of the thread is unwound from the cylinder.

Option: 1

10~Joule


Option: 2

20~Joule


Option: 3

30~Joule


Option: 4

40~Joule


Answers (1)

best_answer

Taking angular impulse about the centre of mass
\gamma F(\Delta t)=I \omega


For translatory motion

\begin{aligned} F(\Delta t)&=m U_{CM} \\ r\left(m v_{CM}\right)&=\left(m r^2\right) \omega \\ v_{CM}&=r \omega \\ \omega&=\frac{v_{CM}}{r} \\ \frac{d \theta}{d t}&=\frac{d x}{d t(r)} \\ (d x)&=r(d \theta) \end{aligned}

The effective velocity of point P

\begin{aligned} v_p&=v_{CM}+r \omega=2 v_{c m} \\ \vec{F} \cdot \vec{v}_p&=P \\ W&=\Delta K \\ (F)\times (2 x)&=K-0 \\ x&=\frac{K}{2 F} \\ K&=2\times10\times0.5 \\ K&=10 \text { Joule } \end{aligned}

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