Question

The rate of change of velocity of a body falling from rest in a resisting medium is described by equation dv by dt=At-Bv . The dimensions of a and b are

Answer 1

Given, dv/dt = At - Bv
Here , dv/dt is rate of change of velocity , v is velocity and t is time.
So, dimension of A = dimension of {dv/dt}/dimension of the
= [LT⁻²]/[T] = [LT⁻³]
∴ dimension of A = [LT⁻³]

Dimension of B = dimension of {dv/dt}/dimension of v
= [LT⁻²]/[LT⁻¹] = [T⁻¹]
∴ dimension of B = [T⁻¹]

Answer 2

Hello Dear.

Here is the answer---

→→→→→→→→→


Given ⇒

     dv/dt = At - Av

Where,

 dv/dt is the Rate of Change in Velocity.
 v = Velocity
 t = time.

For the Dimensions of A,

∴ Dimension of A = (Dimension of dv/dt)/(dimension of time)
   = [LT⁻²]/[T]
   = [LT⁻³]

For the Dimension of B,

∴ Dimension of B = (Dimension of dv/dt)/(dimension of velocity)
   = [LT⁻²]/[LT⁻¹]
   = [T⁻¹]


→→→→→→→→→


Hope it helps.

Have a Good Day.