wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A plate of mass M is moved with constant velocity v against dust particles moving with velocity u in opposite direction as shown. The density of the dust is ρ and plate area is A. Find the force F required to keep the plate moving with uniform velocity.


A
ρA(u+v)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
ρ(u+v)2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
ρAu2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
ρA(u+v)2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D ρA(u+v)2

Velocity of plate relative to dust = (v+u)
In time dt, the plate comes into contact with volume of dust particles
dV=Adx=A(v+u)dt

So, mass of dust particles striking the plate in time dt is
dm=ρdV=ρA(v+u)dt ...(1)

If we consider (plate + dm mass of dust) as a system and apply impulse momentum equation over time dt,


Change in momentum P=PfPi
P=(M+dm)v[Mvdm.u]
=Mv+dm.vMv+dm.u
=dm.(v+u)
ΔP=F.t
F=dmdt(u+v)

From eq. (1)
F=ρA(v+u)dt.(v+u)dt
F=ρA(u+v)2 is the force acting on the plate due to the dust.
Hence, the same force F is required to keep the plate moving with uniform velocity.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon