Question

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Answer a)
$= 6(v + \frac{wr}{2} ) \div 17r$
b)deltaE =
$\frac{7}{68} m {r}^{2} {w}^{2}$
Want Proper solution .

Answer 1

I'm hurry , so just pasted the solution.
Kindly, understand it.
I may give you bit understanding.

Basic Understanding to do this question :

1) Conservation of Angular Momentum.

2) Conservation of Linear Momentum.

3) Concept of Maxima and Minima.

4) Moment of Inertia

5) Centre of Mass

6) Energy Conservation of Combined Rotational and Translational Motion.

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Final Result :
$1)at \: v \: = wr \: final \\ \: angular \: velocity \: of \: system \: is \: \\ \frac{9w}{17} \: in \: clockwise \: sense. \\ (on \: seeing \: from \: \\ above \: the \: plane \: ) .$\\
2)
E =
$\frac{7}{68} m {w}^{2} {r}^{2}$

3) Amount of Energy lost will be minimum when v =
$\frac{6wr}{5} clockwise \: \\ and \: that \: minimum \: energy \: lost \\ \: is \: \\ \: \frac{m {r}^{2} {w}^{2} }{10} .$
Hope, you understand my answer and it may helps you.

Answer 2

Answer:

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