Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed of the smaller wheel is
Solution
Correct Answer: Option A
let each wheel make x revolutions per sec. Then
\(\left[\left(2\mathrm\pi\ast\frac72\ast\mathrm x\right)+\left(2\mathrm\pi\ast7\ast\mathrm x\right)\right]\ast10=1980\)
\(\left(2\ast\frac{22}7\ast\frac72\ast x\right)+\left(2\ast\frac{22}7\ast\frac72\ast x\right)=198\)
\(66x=198\)
distance moved by smaller wheel in 3 revolutions
\(2\ast\frac{22}7\ast\frac72\ast3=66cm\)
speed of smaller wheel = \(\frac{66}3\) m/s = 22m/s
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