Find the current density when oxygen diffuses through a red cell of thickness 2.5 10-8 cm , the two ends of which are maintain at a fixed concentration C0 .
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Suppose we find the sum of solutions obtained in (i) and (ii) of (b) above. Does this give a solution of the equation describing the motion? If yes, what physical situation, this solution will be correspond to? When is the velocity of the pendulum maximum? What type of energy does the pendulum have at position of maximum velocity?
A body of constant mass m is projected vertically upward with an initial velocity v0 in a medium offering a resistance k | v | , where k is a constant. Neglect changes in the gravitational force.
i) Find the maximum height xm attained by the body and the time tm at which this maximum height is reached.
ii) Show that if kv0 /mg < 1, then tm and xm can be expressed as
Consider the following first-order ODE formulation = a{L- n(t)}, n(t0) = n0
.
Associate the variables {t, n(t)} and the parameters {a, L} to a physical system so that the above formulation becomes a mathematical model for population changes.
The rate of increase of susceptible SARS victims is proportional to the number of susceptible persons and number of infected persons. If there are S0 susceptible persons and 1-infected person at a time t0 then
i) set up the equation for the spread of the disease
ii) solve the resulting equation
iii) give a physical interpretation of the same by putting the epidemic curve
iv) write the limitations of this model.
A profit maximizing monopolist produces a quantity of a commodity. His
D(p) = 30 , where p is the price. Find the values of p, q and the profit.
Consider the pay-off table for two players given below
Player B
By graphical procedure determine the value of the game and the optimal mixed strategy foreach player.
The return distribution on 2 securities, A and B is as follows:
| Event (j) | Chance p1 j = p 2 j | Return | |
| R 1 j | R 2 j | ||
| 1 | 0.33 | 19 | 18 |
| 2 | 0.25 | 17 | 16 |
| 3 | 0.17 | 11 | 11 |
| 4 | 0.25 | 10 | 9 |