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?
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In a perfectly competitive market, the supply function S(p) and demand function D(p) are given as follows:
, where p is the price:
i) Find the equilibrium prices
ii) Using Walrasian stability condition, determine whether the equilibrium prices are stable.
A particle is moving under a central attracting force F. Show that its equations of motion can be written as
where
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
A particle is moving under a central force along the path given by the equation r = a tan .Show that the radial acceleration is
where,
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?
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 |