Two particles of equal mass m have respective
initial velocities $$u\widehat i$$ and $$u\left( {{{\widehat i + \widehat j} \over 2}} \right)$$.
They collide completely inelastically. The energy lost in the process is :

Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm^–2
between A and B where the area of cross section
are 40 cm² and 20 cm², respectively. Find the
rate of flow of water through the tube.
(density of water = 1000 kgm^–3)

Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is 0.7 V. For the input voltages shown in the figure, the voltage (in Volts) at point A is __________.

The distance x covered by a particle in one dimensional motion varies with time t as
x² = at² + 2bt + c. If the acceleration of the particle depends on x as x^–n, where n is an integer, the value of n is __________