Question 1

A centrifuge is used to separate blood components by spinning test tubes at high speeds. What is the primary force responsible for pushing the denser particles outward during centrifugation?

Accepted Answer

Centrifugal force

Question 2

A car moves around a circular track with increasing speed. At a certain instant, its velocity is tangent to the circle. What is the direction of the net acceleration at that instant?

Accepted Answer

A combination of inward (centripetal) and tangent (due to increasing speed)

Question 3

In a random walk in one dimension, a molecule can move left, right, or stay still in each time step. After 3 steps, how many possible paths are there for the molecule to end up at $$x = -1$$?

Accepted Answer

4

Question 4

Which of the following best describes the difference between directed and random motion?

Accepted Answer

Directed motion has a consistent direction, while random motion results from unpredictable collisions.

Question 5

A histogram of the final positions of 1000 molecules after 100 steps of random walk is centered at zero. What does the center of this histogram represent?

Accepted Answer

The mean position, $$x_{avg}$$

Question 6

What does the root-mean-square (RMS) distance, $$x_{rms}$$, represent in the context of diffusion?

Accepted Answer

The average distance a molecule travels from the origin

Question 7

The RMS distance for a diffusing molecule in one dimension is given by $$x_{rms} = \sqrt{2Dt}. If $$the diffusion constant $$D is $$doubled, what happens to $$x_{rms}$$ after the same time $$t$$?

Accepted Answer

$$x_{rms}$$ increases by a factor of $$\sqrt{2}$$

Question 8

If you increase the number of molecules in a random walk experiment (keeping the number of steps fixed), what happens to the histogram of final positions?

Accepted Answer

The histogram becomes smoother and more symmetric

Question 9

In a cell membrane, there are more sodium ions inside the cell than outside. If the membrane is permeable to sodium, what is the net movement of sodium ions?

Accepted Answer

More ions move out of the cell

Question 10

Which equation best describes the probability distribution for the final position $$x of a $$large number of particles after a random walk?

Accepted Answer

$$P(x) \propto e$$^{-\frac{(x-x_{avg}$$)^2$$}{x_{rms}^2}}$

Question 11

A baseball is hit with the same initial velocity in two scenarios: one with air resistance (drag) and one without. Which statement is correct about the trajectories?

Accepted Answer

With drag, the baseball travels a shorter distance and reaches a lower height.

Question 12

In a random walk, what is the effect of increasing the number of steps $$N on $$the RMS distance?

Accepted Answer

The RMS distance increases as $$\sqrt{N}$$

Question 13

Which of the following is a correct interpretation of the standard deviation in a histogram of particle positions after diffusion?

Accepted Answer

It is the average distance from the mean position.

Question 14

A molecule undergoes a random walk in two dimensions. What is the formula for the RMS distance from the origin after time $$t$$?

Accepted Answer

$$r_{rms} = \sqrt{4Dt}$$

Question 15

Which of the following best explains why balls in a Plinko board simulation are most likely to end up in the middle slots after many trials?

Accepted Answer

There are more possible paths that lead to the middle slots.

Question 16

If the mean position $$x_{avg} of a $$histogram is not zero, what does this indicate about the motion of the particles?

Accepted Answer

There is a net directed motion.

Question 17

Which of the following factors does NOT affect the diffusion constant $$D$$?

Accepted Answer

The color of the molecule

Question 18

A histogram of final positions for a random walk experiment becomes narrower as:

Accepted Answer

The number of molecules increases

Question 19

Which of the following is the best model for the spread of perfume molecules in a room?

Accepted Answer

Random motion (diffusion)

Circular and Random Motion: Physics with Algebra Study Notes

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