question_answer

A point P on the rim of a wheel is initially at rest and in contact with the ground. Find the displacement of the point P if the radius of the wheel is 5m and the wheel rolls forward through half a revolution:

A)  5 m                                       

B)  10 m    

C)         2.5m                                    

D)  \[5\left( \sqrt{2{{\pi }^{2}}+8} \right)\]

E)  \[5\left( \sqrt{{{\pi }^{2}}+4} \right)\]

Correct Answer: E

Solution :

                                Net displacement \[s=\sqrt{(\pi {{r}^{2}})+{{(2r)}^{2}}}=\sqrt{{{(\pi \times 5)}^{2}}+{{(2\times 5)}^{2}}}\]                                 \[=5\sqrt{{{\pi }^{2}}+4}\]