Home
Class 11
PHYSICS
Consider a collection of a large number ...

Consider a collection of a large number of particles each with speed v. The direction of velocity is randomly distributed in the collection. Show that the magnitude of the relative velocity between a pair of particles averaged over all the pairs in the collection is greater than v.

A

`2V, 4V`

B

`3V, 3V`

C

`5V,V`

D

`4V,2V`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

A large number of particles are moving each with speed v having directions of motion randomly distributed. What is the average relative velocity between any two particles averaged over all the pairs?

Under what condition is the magnitude of the average velocity of a particle moving in onbe dimension smaller than the average speed over same time interval?

A particle is projected with a speed v and an angle theta to the horizontal. After a time t, the magnitude of the instantaneous velocity is equal to the magnitude of the average velocity from 0 to t. Find t.

In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

A particle moves with constant speed v along a regular hexagon ABCDEF in the same order. Then the magnitude of the avergae velocity for its motion form A to

The fig. shows the displacement time graph of a particle moving on a straight line path. What is the magnitude of average velocity of the particle over 10 seconds?

Assertion : Particle A is moving Eastwards and particle B Northwards with same speed. Then, velocity of A with respect to B is in South-East direction. Reason : Relative velocity between them is zero as their speeds are same.

The velocity of a particle moving in the positive direction of x -axis varies as v = alpha sqrt(x) where alpha is positive constant. Assuming that at the moment t = 0 , the particle was located at x = 0 , find (i) the time dependance of the velocity and the acceleration of the particle and (ii) the mean velocity of the particle averaged over the time that the particle takes to cover first s meters of the path.

The velocity of a particle moving in the positive direction of the x axis varies as v=alphasqrtx , where alpha is a positive constant. Assuming that at the moment t=0 the particle was located at the point x=0 , find: (a) the time dependence of the velocity and the acceleration of the particle, (b) the mean velocity of the particle averaged over the time that the particle takes to cover the first s metres of the path.

Two cars are moving is one a same line dimension in opposite direction with the same speed v. The relative velocity of two cars w.r.t. each other is