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A block of mass \mathrm{m} is attached to the pulley disc of equal mass \mathrm{m}  and radius r by means of slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of \mathrm{v}. Find its velocity when the string becomes taut.


 

Option: 1

\mathrm{\frac{v}{3}}
 


Option: 2

\mathrm{\frac{2v}{3}}


Option: 3

\mathrm{\frac{v}{2}}

 


Option: 4

\mathrm{2 v}


Answers (1)

best_answer

Using conservation of angular momentum about the hinge. If \mathrm{v^{\prime}} is the required velocity then

\mathrm{L =m v^{\prime} r+I_c \omega }

\mathrm{ { mvr } =m v^{\prime} r+I_c \omega }

\mathrm{{ mvr } =m v^{\prime} r+\frac{m r^2}{2} \times \frac{v^{\prime}}{r}}
Divide \mathrm{m\gamma} both sides-

\mathrm{v=v^{\prime}+\frac{m v^{\prime}}{2}=\frac{3 v^{\prime}}{2}}

\mathrm{v^{\prime}=2v/2}

Hence option 2 is correct.
 

Posted by

Divya Prakash Singh

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