A parallel beam of particles of mass `m` moving with velocity `v` impinges on a wall at an angle `theta` to its normal. The number of particles per unit volume in the beam is `n`. If the collision of particles with the wall is elastic, then the pressure exerted by this beam on the wall is

Options

A. `2mnv^(2)costheta`
B. `2mnv^(2)cos^(2)theta`
C. `2mn v costheta`
D. `2mn v cos^(2)theta`

Answer

B

Explanation

The change number of particle `n` volume `dvsdx is dN =ndv=ndsx`

`:. Dm=mdN=mnsdx`
`:. (dm)/(dt)=mns(dx)/(dt)=mnsv`
: `F=(dp)/(dt)=/_\v(dm)/(dt)`
`F(2vcostheta)mnsv`
`F-2mnv_(2)scostheta`
`:.` pressure `p=(vecF.vecs)/s^(2)`
`p=(Fscostheta)/(s^(2))=(Fcostheta)/s=2mnv^(2)cos^(2)theta`