Solutions:

Allow a machine to overcome a load L by exerting effort E. Let dE be the effort displacement and dL be the load displacement in time t.

Then, work input and output becomes :

Work input = effort × displacement of effort = E × d_E

Work output = load × displacement of load = L × d_L

We know that the expression for efficiency is –

Efficiency η = work output / work input

Therefore, η = (L × d_L) / (E × d_E) = L / E × d_L / d_E

Or, η = L / E × 1 / (d_E / d_L)

But we know that – L / E = M.A.

Therefore, d_E / d_L = V.R.

Upon substituting values, we get :

η = M.A. / V.R.

Or, we ca write : M.A. = V.R. × η