Question

A block of mass m=2 kg is placed on a plank of mass M=10 kg which is placed on a amooth horizontal plane. The coeffiof friction btwb the block and the plank is 1/3. If a horizontal force F is applied on the blank then find the maximum value of F
for which the block and the plank move together.

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

Answer 2

Answer:

Explanation:

acceleration of system for which they move together

acceleration = F/12

friction acting on them = F/6

friction on them should be less than or equals limiting ones

F/6<20/3

F<40