Two particles are projected from a point at the same instant with velocities whose horizontal and vertical components are `u_(1), v_(1)` and `u_(2), v_(2)` respectively. Prove that the interval between their passing through the other common point of their path is
`(2(v_(1)u_(2) - v_(2) u_(1)))/(g (u_(1) + u_(2))`

Two particles are projected simultaneously in the same vertical plane, from the with speed u_(1) and u_(2) at angle of projection theta_(1) and theta_(2) respectively with the horizontal. The path followed by one, as seen by other (as long as both are in flight), is

The molecular velocities of two gases at same temperature are u_(1) and u_(2) , their masses are m_(1) and m_(2) respectively, which of the following expression is correct ?

Find the points of discontinuity of y = (1)/(u^(2) + u -2) , where u = (1)/(x -1)

Two coil have self-inductances L_(1)=8 mH and L_(2)=2 mH . In both of them currents are increased at the same constantt rate. At a certain instant the power given to the two coils is the same. If, at that instant, I_(1), V_(1), U_(1) and I_(2), V_(2), U_(2) be the currents, induced voltages and energies stored in the two coils respectively, then ltbr. (a) I_(1)//I_(2)=1//4 (b) I_(1)//I_(2)=4 (c) W_(2)//W_(1)=4 (d) V_(2)//V_(1)=1//4 .

Two stones are thrown vertically upwards simultaneously with their initial velocities u_(1) and u_(2) respectively. Prove that the heights reached by them would be in the ratio of u_(1)^(2) : u_(2)^(2) (Assume upward acceleration is -g and downward acceleration to be + g ).

A particle is projected with a velocity u making an angle theta with the horizontal. At any instant its velocity becomes v which is perpendicular to the initial velocity u. Then v is