Question

A block of mass m= 2 kg is placed on a plank of mass M = 10 kg which is placed on a

smooth horizontal plane. The coefficient of friction between the block and plank is 1/3. If a horizontal force F is applied on the plank, then the minimum value of F for which the block and plank move together is
(a) 30N
(b) 40N
(c) 120N
(d) None of the above

Answer 1

answer : option (b) 40N

explanation : Let a is the acceleration of system of block and plank.

now see free body diagram to understand better.

for block,

frictional force = umg = ma .....(1)

or, a = ug

given, u = 1/3 and g = 10 m/s²

so, a = 10/3 m/s²

for plank,

F - frictional force = Ma

or, F - ma = Ma  [ from equation (1), ]

or, F = (m + M)a

now putting, a = 10/3 m/s², m = 2kg and M = 10kg

so, F = (2 + 10) × 10/3 = 40 N

hence, minimum force is 40N