Question

A plank of mass M is placed on a rough horizontal surface. A man of mass m walks on the plank with an acceleration 'a' while the plank is also acted upon by a horizontal force F whose magnitude and direction can be adjusted to keep the plank at rest :

the coefficient of friction between plank and surface is μ. Choose the correct options

(A) The maximum value of F to keep plank at rest is ma + μ(M + m)g

(B) The minimum value of F to keep the plank at rest is ma – μ(M + m)g

(C) The direction of friction on ground due to plank will always be forward

(D) If F = ma then friction on man due to plank is also F and friction between plank and ground will be zero

Answer 1

Correct option (A)(B)(C)

Explanation:

If F > f then friction due to gravity will be left

Fmax = f + (M + m)g = ma + (M + m)g

If F < f then friction due to gravity will be right

Fmin = Ma – m(m + M)g

If F = ma

⇒ f = ma = f