CEdwardIn case of revolutions or circular motion, 1 rev = 2πr (time taken for 1 revolution)
Time is also directly proportional with diameter (T ∝ D), So if diameter is doubled, time taken will be doubled. A larger wheel will take more time to complete a revolution (2πr) than the smaller wheel.
Time is inversely proportional to speed for constant work (T = 1/S)
If time is doubled, speed is half (speed is inversely proportional to D and T)
From statement 1 & statement 2 - If speed of smaller gear is 600 RPM, then speed of larger will be half i.e 300 RPM
Also question gives a hint "the larger gear is guaranteed to last how many days longer than the smaller gear" means larger gear will take more time and therefore rotate at a slower speed than the smaller gear
CEdward wrote:
PrashantPonde wrote:
Each gear has life to 6,000,000,000 revolutions. As both gears are interlocked, smaller gear will have more revolutions and will wear out before the larger one.
(1) The diameter of the larger gear is twice the diameter of smaller gear.
INSUFFICIENT: This means - the circumference of the larger gear is twice that of smaller gear. I.e. 1 revolution of larger gear = smaller gear rotates two times.
Even if we know relative ratio for diameters, we don’t know what rate at they are revolving per minute.
- If the gears are rotating at extreme high speed, they will wear out soon -> hence difference of their life (in minutes) will be smaller.
- If the gears are rotating at extreme slow speed, they will last lot longer -> hence difference of their life (in minutes) will be much larger.
Hence we cannot conclude how many days the gears will last long.
(2) The smaller gear revolves 600 times per minute.
INSUFFICIENT: This information is clearly insufficient. This tells the revolution rate only for smaller gear. No info about larger gear (speed or relative diameter ratio)
Combining (1) & (2)
SUFFICIENT: As we know smaller gear has 600 RPM and 1/2 the diameter than larger one -> the larger gear rotate at half the speed i.e. 300 RPM and hence we can find out how many days they can last long.
We can stop at this point (no need to calculate further during actual exam) but just for sake of curiosity lets calculate further:
No of days larger gear lasts longer than smaller gear = \(\frac{6,000,000,000}{24*60*60 minutes} * (\frac{1}{300}-\frac{1}{600}) = 115.74 days.\)
Hence choice(C) is the answer.
Can somebody explain the leap in logic here?
Why does twice the circumference equate to a halving of the speed?
Bunuel?
close
15 Oct 2020, 10:03
