GATE Papers >> Mechanical >> 2015 >> Question No 237

Question No. 237 Mechanical | GATE 2015

Figure shows a wheel rotating about O2. Two points A and B located along the radius of wheel have speeds of 80 m/s and 140 m/s respectively. The distance between the points A and B is 300 mm. The diameter of the wheel (in mm) is__________


Answer : 1390 to 1410


Solution of Question No 237 of GATE 2015 Mechanical Paper

$V_A=r_{A\cdot w}=80\;m/s$

$V_B=r_{b/cdot w}=140\;m/s$

$\frac{r_b}{v_b}=\frac{r_A}{v_A}\;\;\;\therefore r_b=\left(\frac{v_B}{v_A}\right)\cdot r_A=\left(\frac{140}{80}\right)\cdot r_A=1.75\;r_A$

we have given $r_b-r_A=300$

                               $1.75\;r_A-r_A=300$

                        $r_A=300/0.75=400$

      so,$r_b=300+r_A=300+400+700\;mm$

$\therefore$ Dia. of wheel is 1400 mm . 

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