Question

Find the percentage change in the number of revolutions made in a distance of 1 km by a wheel of diameter 15 cm, when its radius is increased by 0.25 cm.

पर्याय

• decrease by 3.3%

• decrease by 30%

• increase by 10%

• None of these

Answer 1

decrease by 3.3%

Explanation:

Original radius of wheel = `15/2` = 7.5 cm

One revolution will cover a distance equal to 2πr.

Which equals to 2π (7.5) = 15π cm

When radius is increased by 0.25 cm,

New radius = 7.5 + 0.25 = 7.75 cm

Distance covered in one revolution = 2π (7.75) = 15.5π

Let us assume that originally, the wheel was making 10 revolutions (in a km), then total distance = 15π (10) = 150π

No. of revolutions with increased radius = `(150π)/(15.5π)` = 9.67

There is decrease in no. of revolutions (obviously)

% decrease = `(10 - 9.67)/10 xx 100`

= 3.3%