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

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(D) The circumference of the smaller wheel is $C_1 = \pi d_1 = 7\pi \,cm$.
The circumference of the larger wheel is $C_2 = \pi d_2 = 14\pi \,cm$.
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Vedclass · Accepted Answer

Quantity $I = $ Quantity $II$ (or relationship cannot be established)

Vedclass · Answer

(D) The circumference of the smaller wheel is $C_1 = \pi d_1 = 7\pi \,cm$.
The circumference of the larger wheel is $C_2 = \pi d_2 = 14\pi \,cm$.
Let $n$ be the number of revolutions per second made by both wheels.
The speed of the smaller wheel is $v_1 = 7\pi n \,cm/s$ and the speed of the larger wheel is $v_2 = 14\pi n \,cm/s$.
Since they move towards each other,their relative speed is $v_1 + v_2 = (7\pi n + 14\pi n) = 21\pi n \,cm/s$.
They meet after $10 \,s$ over a distance of $1990.50 \,cm$.
Therefore,$(21\pi n) 	imes 10 = 1990.50$.
$210\pi n = 1990.50$.
$n = \frac{1990.50}{210\pi} = \frac{1990.5}{210 	imes (22/7)} = \frac{1990.5 	imes 7}{210 	imes 22} = \frac{13933.5}{4620} = 3.0159 \dots$ (approx $3$ revolutions per second).
Speed of smaller wheel $= 7\pi 	imes 3 = 21\pi \,cm/s$.
Thus,Quantity $1 = 21\pi \,cm/s$,which is equal to Quantity $2$.

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