Is the space between the particles in the matter influence the speed of diffusion? Explain. `(AS_2)`

Two particle P and Q describe S.H.M. of same amplitude a same frequency f along the same straight line .The maximum distance between the two particles is asqrt(2) The phase difference between the two particle is

If the gravitational force between two objects were proportional to 1/R (and not as 1/R^2 ) where R is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed v_1 proportional to .........

The potential energy of a particle of mass 1 kg moving along x-axis given by U(x)=[(x^(2))/(2)-x]J . If total mechanical energy of the particle is 2J then find the maximum speed of the particle. (Assuming only conservative force acts on particle)

The distance between two particles of masses m_(1)andm_(2) is r. If the distance of these particles from the centre of mass of the system are r_(1)andr_(2) respectively, then show that r_(1)=r((m_(2))/(m_(1)+m_(2)))andr_(2)=r((m_(1))/(m_(1)+m_(2)))

Two particles of mass m_(1) and m_(2) are projected from the top of a tower. The particle m_(1) is projected vertically downward with speed u and m_(2) is projected horizontally with same speed. Find acceleration of CM of system of particles by neglecting the effect of air resistance.

A particle of mass m and charge +q approaches from a very large distance towards a uniformly charged ring ofradius Rand charge, mass same as that of particle, with initial velocity v_(0) along the axis of the ring as shown in the figure-1.420. What is the closest distance of approach between the ring and the particle? Assume the space to be gravity free and frictionless :

A particle of mass m and charge (-q) enters the region between the two charged plates initially moving along x-axis with speed v_x (like particle 1 in figure. The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL^(2)//(2m v_(x)^(2)) . Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.

Explain particle-wave (dual) nature of matter.