Question 72

Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposit directions. Both of them make same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is

Solution

Distance covered by big wheel in 1 revolution = $$2\pi r$$

= $$2\times\frac{22}{7}\times7=44$$ cm

and by small wheel = $$22$$ cm

Since, distance $$\propto$$ speed

Let speed of small wheel = $$x$$ cm/s, => Speed of big wheel = $$2x$$ cm/s

Also, relative speed of both wheels = $$\frac{1980}{10}=198$$ cm

=> $$x+2x=198$$

=> $$x=\frac{198}{3}=66$$ cm/s

=> Ans - (C)

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