Question

A particle is moving along circle with uniform speed. In moving from one point to a diametrically opposite point, the ratio of magnitude of change in velocity to change in magnitude of velocity is what?

Answer 1

Ratio of magnitude of change in velocity to change in magnitude of velocity = 1:m

Explanation:

Given: A particle is moving along circle with uniform speed. Moving from one point to a diametrically opposite point.

Find: The ratio of magnitude of change in velocity to change in magnitude of velocity.

Solution:

Given that the particle is moving to a diametrically opposite point, so the velocity will be displacement by time = diameter/ time = 2r/t.

Momentum =  mass * velocity =  mv = m*2r/t

Ratio = 2r/t : m *2r/t = 1:m

Answer 2

Given that,

A particle is moving along circle with uniform speed.

A particle moves one point to opposite point.

Let the velocity of particle at one point

$v_{1}=v$

The velocity of particle at opposite point

$v_{2}=-v$

When particle is moving along circle with uniform speed from point P to point Q

We need to calculate the change in velocity

Using formula of velocity

$\Delta v=v_{2}-v_{1}$

$\Delta v=-v-v$

$\Delta v=-2v$  

$|\Delta v|=2v$  

The magnitude of velocity of particle is 2v.

When particle is moving along circle with uniform speed from point Q to point P

Now, velocity of particle at Q $v_{1}= -v$

velocity of particle at P $v_{2}= v$

We need to calculate the change in velocity

Using formula of velocity

$\Delta v'=v_{2}-v_{1}$

$\Delta v'=v-(-v)$

$\delta v' = 2v$

We need to calculate the ratio of magnitude of change in velocity

Using formula of change in velocity

$\dfrac{\Delta v}{\Delta v'}=\dfrac{2v}{2v}$

$\dfrac{\Delta v}{\Delta v'}=1:1$

Hence, The ratio of magnitude of change in velocity is 1:1.