Question

A particle is moving along a circular path with a constant speed ‘v’. The change in velocity of the particle in half rotation is

Answer 1

Answer:

Answer

Correct option is

B

2

π

v

The particle starts from point P and after half rotation, it reaches at Q via path PMQ.

Distance covered by particle to reach at Q is d=πR

Time taken, t=

v

d

=

v

πR

Displacement of the particle, s=PQ=2R

∴ Average velocity, v

avg

=

t

s

=

v

πR

2R

=

π

2

v

Answer 2

Concept:

• Uniform circular motion
• Calculating Displacement
• Calculating velocity

Given:

• Speed of particle = v
• The radius of the circle = R

Find:

• Change in velocity of the particle in half rotation

Solution:

• The particle moves along a uniform circular path
• The only acceleration that is acting is the centripetal acceleration
• Since the speed is constant, there is no tangential acceleration
• At the first point, assume the direction of the velocity is to the left
• As the particle completes half a rotation, it is at the diametrically opposite side, so the direction of the velocity is to the right
• So the net change in velocity is v-(-v) = 2v

The change in velocity is 2v.

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