Wheels of diameters 7, cm and 14, cm start ro | vedclass

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Question

(C) Let $n$ be the number of revolutions per second made by both wheels.Circumference of the smaller wheel $(d_1 = 7\, cm)$ is $C_1 = \pi d_1 = 7\pi\,

Vedclass · Accepted Answer

$66$

Vedclass · Answer

(C) Let $n$ be the number of revolutions per second made by both wheels.Circumference of the smaller wheel $(d_1 = 7\, cm)$ is $C_1 = \pi d_1 = 7\pi\, cm$.Circumference of the larger wheel $(d_2 = 14\, cm)$ is $C_2 = \pi d_2 = 14\pi\, cm$.Distance covered by the smaller wheel in $10\, seconds$ is $D_1 = n 	imes C_1 	imes 10 = n 	imes 7\pi 	imes 10 = 70n\pi\, cm$.Distance covered by the larger wheel in $10\, seconds$ is $D_2 = n 	imes C_2 	imes 10 = n 	imes 14\pi 	imes 10 = 140n\pi\, cm$.Since they meet after $10\, seconds$,the sum of the distances covered is equal to the total distance between $X$ and $Y$:$D_1 + D_2 = 1980$$70n\pi + 140n\pi = 1980$$210n\pi = 1980$$n = \frac{1980}{210\pi} = \frac{198}{21\pi} = \frac{66}{7\pi}$ revolutions per second.The speed of the smaller wheel is $v_1 = n 	imes C_1 = \left(\frac{66}{7\pi}ight) 	imes 7\pi = 66\, cm/sec$.

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