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Home » Consider a rectangular block of wood moving with a velocity vo in a gas at temperature T and mass density ρ. Assume the velocity is along the x-axis and the area of cross-section of the block perpendicular to vo is A. Show that the drag force on the block is
Consider a rectangular block of wood moving with a velocity vo in a gas at temperature T and mass density ρ. Assume the velocity is along the x-axis and the area of cross-section of the block perpendicular to vo is A. Show that the drag force on the block is
CBSE | Class 11 | Kinetic Theory | NCERT Exemplar | Physics
Consider a rectangular block of wood moving with a velocity vo in a gas at temperature T and mass density ρ. Assume the velocity is along the x-axis and the area of cross-section of the block perpendicular to vo is A. Show that the drag force on the block is

Exemplar Solutions Physics Class 11 Chapter 13 - 9, where m is the mass of the gas molecule.

Answer:

Let ρm represent the number of molecules per unit volume

Then the expression for the change in momentum by a molecule on front side is

= 2m (v + v0)

Similarly, the expression for change in momentum by a molecule on backside is

= 2m (v – v0)

A number of molecules striking the front side is given as follows:

= 1/2 [A(v+v0)∆t] ρm

The number of molecules striking the backside is

=1/2 [A(v-v0)∆t] ρm

Upon solving the above equation by considering the KE of the gas molecule,

we get the dragging force as follows:

= 4m A ρmv0√kgT/m

i

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