Phase space deagrams are useful tools
.
in analyzing all kinds of dynamical problems. They are especially usrful in studying the changes in motion as initial position and momenum are changed. Here we conseder some simple dynamical systems in one dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is `x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which positon or momentum upwards (or to right) is poitive and downwards (or to left) is negative.
The phace diagram for a ball thrown vertically up from ground is.

Options

A. (a) (##JMA_CHMO_C10_034_O01##).
B. (b) (##JMA_CHMO_C10_034_O02##).
C. (c ) (##JMA_CHMO_C10_034_O03##).
D. (d) (##JMA_CHMO_C10_034_O04##).

Answer

D

Explanation

(d) When the ball is throw upwards, at the point of throw (O) the linear momentum is in upwards derection (and has a maximum value ) and the position is zero. At the time passes, the ball moves upwards and its momentum goes on decreasing and the position becomes zero at the topmost point (A).
(##JMA_CHMO_C10_034_Q01##).
As the time increases, the ball starts moving down with an increasing linear momentum in the downward derection.
These characteristics are represented by graph)^(d).