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  • As given in diagram two paltes A and B move with velocities -V  and 3V . If the sphere does not slide relative to the plate . Assuming mass of each body as m Find the kinetic energy of sphere&

As given in diagram two paltes A and B move with velocities -V  and 3V . If the sphere does not slide relative to the plate . Assuming mass of each body as m Find the kinetic energy of sphere 

 

Option: 1

\frac{12}{5}mv^2


Option: 2

\frac{13}{5}mv^2


Option: 3

\frac{7}{5}mv^2


Option: 4

\frac{9}{5}mv^2


Answers (1)

best_answer

As we have learned

Instantaneous axis of rotation -

Motion of an object may look as pure rotation about a point which has zero velocity.

- wherein

For such a point we can study system as pure rotational motion.

 

 Top point of sphere move with velocity V and bottom point move with velocity 2V 

Position of ICR 

\frac{y}{v} = \frac{2R-y}{3v} \Rightarrow y= R/2

Angular velocity w = v/y = 2v /R

Kinetic energy of sphere =

 \frac{1}{2} I_c w^2 \\\\ = \frac{1}{2} [ \frac{2}{5}MR^2+m(oc)^2]w^2\Rightarrow oc = R-\frac{R}{2} = \frac{R}{2}\\\\k_{rot}= = \frac{1}{2} [ \frac{2}{5}MR^2+m \frac{R^2}{4}]w^2 = \frac{13}{20} w^2R^2m\\\\ K_{rot} = \frac{13}{20} m \left [ \frac{2v}{R} \right ]^2 R^2 = \frac{13}{5}mv^2

 

 

 

 

 

Posted by

Rakesh

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