Question

a body covered a distance along a semicircular path. find the ratio of distance to displacement 1s.(Given radius=5m)

Answer 1

Hey.

Here is the answer.

As body travels 1/2 of a circle 

so, distance covered , d = 1/2 of circumference 

or, d = 1/2 × 2πr

or, d = πr

Displacement D :

As the displacement is shortest path between initial and final position

So , it will be the diameter of the circular path ,

D = 2 r

Hence, ratio will be

or, d : D = πr : 2r

or, d : D = π : 2.

Thanks .

Answer 2

Answer :

Radius of the semicircular path = 5 cm.

Circumference of semicircle = πr.

So, Distance travelled = 3.14*5 = 15.7 cm.

Displacement will be the diameter, that is, 2r = 2*5 = 10 cm.

Hence, Distance = 15.7 cm and Displacement = 10 cm.

So, ratio of distance to displacement = 15.7/10 = 1.57 cm.

Additional Information :

• Distance is the total length of the path travelled by the body.

• Displacement is the shortest distance between the initial position and the final position of the body.

• Distance is a scalar quantity whereas displacement is a vector quantity.

• The magnitude of distance is equal to or greater than the magnitude of displacement.

• Speed is said to be the distance travelled per unit time.

• Velocity is the displacement per unit time.

• Speed is a scalar quantity whereas velocity is a vector quantity.