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  • Two solid cylinders are connected by a massless rod as shown in the figure. The distance b/w centre line of both cylinders is 3R. what is the moment (in terms of  MR2) of inert

Two solid cylinders are connected by a massless rod as shown in the figure. The distance b/w centre line of both cylinders is 3R. what is the moment (in terms of  MR2) of inertia of the system about the axis shown in the below diagram?

Option: 1

5.55


Option: 2

6.25


Option: 3

1.85


Option: 4

1.6


Answers (1)

best_answer

As we have learned

Moment of inertia for solid cylinder About axis passing through central line is given by

I_c=\frac{1}{2} MR^{2}

For the figure

For cylinder 1

 I_1 = I_c + Md^2 \\\\I_1 = \frac{1}{2} MR^2 + M \left [ R + \frac{R}{3} \right ]^2\\\\ \frac{1}{2}MR^2 + M [\frac{4R}{3}]^2 = \frac{41}{18} MR^2

For cylinder 2

I_2 = I_c + Md^2 \\\\I_2 = \frac{1}{2} MR^2 + M \left [ R + \frac{2R}{3} \right ]^2\\\\I_2= \frac{59}{18} MR^2

So

I = I_1 + I_2 = \frac{41}{18}MR^2+ \frac{59}{18}MR^2 = \frac{100}{18}MR^2= \frac{50}{9}MR^2

 

 

 

 

Posted by

Rakesh

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