Imagine a gravity free laboratory, in outer space, where you are asked to study the motions of a large number of marbles kept in a transparent cubical jar, as you give the jar quick, small jerks in random directions. You will observe, that after giving a sufficient number of jerks, the marbles start moving rather chaotically, i.e., each marble bounces off other marbles every now and then, and takes a random trajectory between two points due to these collisions. You seem to have given some kinetic energy to each marble, when the jar was being shaken. What happens when you release the jar suddenly, leaving it suspended in space? Assume all collisions between the marbles to be perfectly elastic.
Imagine a gravity free laboratory, in outer space, where you are asked to study the motions of a large number of marbles kept in a transparent cubical jar, as you give the jar quick, small jerks in random directions. You will observe, that after giving a sufficient number of jerks, the marbles start moving rather chaotically, i.e., each marble bounces off other marbles every now and then, and takes a random trajectory between two points due to these collisions. You seem to have given some kinetic energy to each marble, when the jar was being shaken. What happens when you release the jar suddenly, leaving it suspended in space? Assume all collisions between the marbles to be perfectly elastic.
The correct option is C The jar starts shaking with small, random vibrations
When you have shaken the jar, the walls hitting the marbles will impart some momenta and kinetic energies on them. The marbles will collide with each other, but perfectly elastically, which means the total kinetic energy transferred to all the marbles combined will be unchanged, only individual energies will be exchanged between one marble and another when they collide.
When the jar is left suspended in space after shaking, the marbles will continue to have those kinetic energies, and move about in random directions.
On a large time scale (∼ few seconds) the number of marbles hitting the left wall, say, will equal the number hitting the right wall, resulting in no overall horizontal motion. You could say the same for the vertical direction. Does it mean, then, that the jar has no motion at all? Well, no.
For shorter time scales, there will always be small differences in the numbers of marbles hitting opposite walls. If the right wall gets n impulses in a short time Δt and the left wall gets (n+m)impulses, the jar will move a little towards the left. In the next interval Δt, the jar has an equal probability of moving a little to the right. The same can be said for the top and bottom directions. This is the essence of Brownian motion - the small, jittery motion of the jar due to a large random distribution of similar momentums (the marbles). Hence option (c) is correct.
Gas molecules behave similarly inside a closed volume.
The jar starts shaking with small, random vibrations
When you have shaken the jar, the walls hitting the marbles will impart some momenta and kinetic energies on them. The marbles will collide with each other, but perfectly elastically, which means the total kinetic energy transferred to all the marbles combined will be unchanged, only individual energies will be exchanged between one marble and another when they collide.
When the jar is left suspended in space after shaking, the marbles will continue to have those kinetic energies, and move about in random directions.
On a large time scale (∼ few seconds) the number of marbles hitting the left wall, say, will equal the number hitting the right wall, resulting in no overall horizontal motion. You could say the same for the vertical direction. Does it mean, then, that the jar has no motion at all? Well, no.
For shorter time scales, there will always be small differences in the numbers of marbles hitting opposite walls. If the right wall gets n impulses in a short time Δt and the left wall gets (n+m)impulses, the jar will move a little towards the left. In the next interval Δt, the jar has an equal probability of moving a little to the right. The same can be said for the top and bottom directions. This is the essence of Brownian motion - the small, jittery motion of the jar due to a large random distribution of similar momentums (the marbles). Hence option (c) is correct.
Gas molecules behave similarly inside a closed volume.
