please solve it and explain it in details..
it's a jee advanced problem
Answers
is problem ko hum solve karenge using Centre of mass concept. Agar hum dono charged particles ko as a system manay then the only external force acting on this system is force of gravity.
The internal force acting on the particles is electrostatic Force . Abh agar hum centre of mass a concept use kare then dono particles ka jo mass hai woh same hai iska matlab com (center of mass) jo hai woh dono particles k bich ka jo distance hai uske bich may lie karega i.e.( h2 - h1 ) / 2
Abh ground say agar dekhe then distance of com from the ground is = (distance of particle at the highest point i.e. h2) - (distance of com from the highest particle i.e. (h2 - h1 )/2
toh ground say distance of com is (h1 + h2) / 2
Abh yeah com jo hai woh parabolic path may move karega becoz both the particles will move in parabolic path i.e. projectile motion show karenge
horizontal range diya hua hai L of the first particle so time taken by the first particle to land i.e. time of flight= L/v= Range/velocity in horizontal direction (constant velocity)
ab is time t = L/v may com distance cover karega in vertical direction i.e. kitna niche ki taraf shift hoga
= initial height of the Com - t time may kitna niche aya
= (h1+h2)/2 - 1/2 ×g×(L/v)^2
toh itna niche ajayega .
Ab hum jante hai ki distance of com mass from ground is (H1+H2)/2 , toh ab jab first particle ground ko touch karlega then H1 = 0 i.e. height of first particle from the ground...... so height of com = H2/2
now
H2/ 2 = (h1+h2)/2 - 1/2g(L/v)^2
so we get
H2 = (h1+h2) - g(L/v)^2
yaha par H1 is final distance of first particle from the ground and H2 is the distance of second particle from the ground so obviously hum jante hai ki com dono particles k bich may hai toh (H1+H2)/2 hoga
when first ball touches the ground H1 is zero and com is at a distance H2/2 from the ground or from second particle
