A motor boat of mass m moves along a lake with velocity V₀ .At t = 0, the engine of the boat is shut down. Magnitude of resistance force offered by the boat is equal to rV. Find its acceleration in m/s² when passing through the point x = 2m ( Ans : mV₀/2r )

The answer given viz acceleration at x = 2m  is mV_o/2r  is erroneous.

The formula is dimensionally incorrect.

Given

Force = rV

Let Dimensions of r be [M^xL^yT^z]

MLT^-2 =[M^xL^yT^z][LT^-1]

Comparing

Dimension of r = [MT^-1]

Now given formula

Acceleration = mV_o/2r

LHS

Acceleration = [LT^-2]

RHS

mV_o/2r  = [M][LT^-1]/[MT^-1] = [L]

Which is dimension of length not acceleration.

Again if we consider 2 to have a dimension of length (as x = 2m has been given)

Then too, [L]/[L]= dimensionless

LHS≠RHS

A formula dimensionally incorrect is impossible to hold.

To find the acceleration at x = 2m