question_answer

A massive disc of radius R is moved with a constant velocity m on a frictionless table. Another small disc collides with it elastically with a speed of\[{{v}_{0}}= 0.3 m/s\], the velocities of the discs being parallel. The distance (/shown in the figure is equal to R/2, friction between the discs is negligible. For which u (in m/s) will the small disc move perpendicularly to its original motion after the collision?          

A) 0.1

B) 0.5        

C) 1.0

D) 0.01   

Correct Answer: A

Solution :

[a]\[{{\operatorname{V}}_{0y}}={{V}_{0}} sin \theta \], this component does not change \[{{v}_{0x}} = {{v}_{0}} cos\theta  and u cos \theta \] For elastic collision relative velocity before collision is equal to relative velocity after collision along \[x-axis\] \[{{v}_{0}}\cos \,\theta -u\text{ }cos\text{ }\theta =u\text{ }cos\theta +{{v}_{x}}\] \[\operatorname{If}\,\,{{v}_{x}} cos\theta ={{v}_{0y}}Sin\theta \] By solving \[m=0.1\]