Question

A wheel rotates making $20$ revolutions per second. If the radius of the wheel is $35\, cm$, what linear distance does a point of its rim traverse in three minutes? (take $\pi = 22/7$)

• A. $7.92\, km$
• B. $7.70\, km$
• C. $7.80\, km$
• D. $7.85\, km$

Answer 1

The Correct Option is A

Radius of the wheel $= 35 \,cm$ $\therefore$ Circumference of the wheel $=2\pi\times35\,cm=220\,cm$. Hence, the linear distance travelled by a point of the rim in one revolution $= 220\, cm$. Number of revolutions made by the wheel in $3$ minutes $= 20 \times 3 \times 60 = 3600$. $\therefore$ The linear distance travelled by a point of the rim in $3$ minutes $= 220 \times 3600 = 792000\, cm = 7.92\, km$.

Answer 2

Given:
Radius of the wheel \(= 35 \, \text{cm}\)
Circumference of the wheel \(= 2\pi \times 35 \, \text{cm} = 220 \, \text{cm}\)
Revolutions per second = 20
Time = 3minutes
Convert time to seconds:
\(\text{Time in seconds} = 3 \times 60 = 180 \text{ seconds}\)

Calculate the number of revolutions in 3 minutes:
\(\text{Total revolutions} = 20 \times 180 = 3600\)

Calculate the total distance traveled by a point on the rim:
\(\text{Total distance} = \text{Total revolutions} \times \text{Circumference} = 3600 \times 220 \, \text{cm}\)

Convert centimeters to kilometers:
\(\text{Total distance in kilometers} = \frac{3600 \times 220}{100000} = 7.92 \, \text{km}\)

So, the correct option is (A): 7.92km