question_answer

A ball of mass m moving with a velocity u rebounds from a wall with same speed. The collision is assumed to be elastic and the force of interaction between the ball and wall varies as shown. Then the value of \[{{F}_{0}}\] is -

A) mu/T                

B) 2mu/T

C) 4 mu/T             

D) mu/2T

Correct Answer: C

Solution :

\[z\mathbf{1}.~~~~~~~~~~~Area\text{ }under\text{ }the\text{ }F\text{ }-1\text{ }curve\text{ }=\text{ }Impulse\] \[\frac{{{F}_{0}}T}{2}\] = change in momentum                 \[\frac{{{F}_{0}}T}{2}\,\,=\,\,\,2mu\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\because \,\,\theta =180{}^\circ )\] \[\therefore \,\,\,{{F}_{0}}\,\,=\,\,\frac{2mu}{T}\]