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  • A hollow pipe of mass 'm' and radius 'r' supported by a massless string tightly wind over it. A constant force is

A hollow pipe of mass 'm' and radius 'r' supported by a massless string tightly wind over it. A constant force is applied through the string such that the pipe remains at its position. 

Find the length of the string unwound at time, t=t_{0}. (Given, acceleration due to gravity = g)

Option: 1

\frac{1}{2} g t_{0}^{2}

 


Option: 2

g t_{0}^{2}


Option: 3

\quad \frac{2}{3} g t_{0}^{2}


Option: 4

\frac{3}{4} g t_{0}^{2}


Answers (1)

for translator equilibrium

F=mg

Taking torque a bout the centre of mass -

 c=r F \\c=r F \\

 \alpha\left(m r^{2}\right)=r F \\

\alpha=\frac{r F}{m r^{2}}=\frac{r(\not m g)}{\not m\left(r^{2}\right)}=\frac{g}{r}

Angular displacement of the pipe at t=t_{0}

 \theta=\omega_{0} t+\frac{1}{2} \alpha t^{2} \\

\theta=\frac{1}{2}\left(\frac{g}{r}\right) t_{0}^{2}

Length of the string unwound from the pipe be ' L '

L=R \theta=\left(\frac{g t_{0}^{2}}{2 r}\right) r=\frac{1}{2} g t_{0}^{2}

 

Posted by

Ramraj Saini

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