Question

2
An insect moves for 20 minutes along the
circumference of a circular clock of
diameter 20cm. Displacement and distance
of the insect are

Answer 1

Given : An insect moves for 20 minutes along the circumference of a circular clock of diameter 20 cm.

To find : displacement and distance of the insect are....

solution : displacement = final position - initial position = minimum seperation between two points

here insects move along the circumference of a circular clock.

in 60 minutes, angle made by minute hand = 360°

in 20 minutes, angle made by minute hand = 360/60 × 20 = 120°

see figure, if insect moves from A to B.

then displacement of the insects = AB = 2rsin60°

= 2r × √3/2 = √3 × r

here r = diameter/2 = 20/2 = 10cm

so, displacement of the insect = 10√3 cm

distance is the length of path covered by the object.

distance of the insect = 2πr/360° × 120°

= 2πr/3

= 2 × 3.14 × 10/3

= 20.93 cm

Therefore the distance covered by the insect is 20.93 cm .