Question

Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and 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 10 seconds , the speed of the smaller wheel is :
A. 22 cm/sec
B. 44 cm/sec
C. 66 cm/sec
D. 132 cm/sec

Answer 1

Correct Answer - C
Let each wheel make x revolutions per sec . Then
`[(2pi xx (7)/(2) xx x) + (2pi xx 7 xx x)] xx 10 = 1980`
`implies ((22)/(7) xx 7 xx x) + ( 2 + (22)/(7) xx 7 xx x) = 198`
`implies 66 x = 198 implies x = 3`.
Distance moved by smaller wheel in 3 revolutions
` = ( 2 xx (22)/(7) xx (7)/(2) xx 3)` cm/sec . = 66 cm/sec .