Test Index

Work, Power & Energy

Section: Physics

Question : 7 of 22

Marks: +1, -0

A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true?

[JEE Adv 2017 P1]

The pressure difference between the leading and trailing faces of the plate is proportional to uv
The plate will continue to move with constant non-zero acceleration, at all times
At a later time external force F balances the resistive force
The resistive force experienced by the plate is proportional to v

Validate

Solution:

Molecules hitting the forward and rear surfaces will bounce back with speeds given above. Let mass of one molecule be

m_0

. Then,

\Delta P_0(\text{forward})=2m_0(u+v)

\Delta P_0(\text{Rear})=2m_0(u-v)

Let the rates of collision with front and rear surfaces be

R_1

and

R_2

respectively

So,

R_1\alpha(u+v)

R_2\alpha(u-v)

Force

\Delta P.R.

So,

F_1R_1.2m_0(u+v),F_2=R_2.2m_0(u-v)

So,

F_1-F_2\alpha2m_0(u+v^2)-2m_0(u-v)^2

\alpha\;\;2m_0[4uv]

\alpha\;\;\;uv

so, (A) is correct

Clearly, the net force due to gas is proportion to v, i.e. it is variable hence acceleration of plate is variable. Finally the plate will start moving with terminal velocity

Hence (C) is correct

Resistive force

=\Delta P.A\propto V

⇒ Hence (D) is correct

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