Question

A constant force F is applied in horizontal direction as shown. The contact force between M and m is N and between m and M’ is N’ then:

A) N = N’
B) N>N’
C) N’>N
D) Cannot be determined

Answer 1

Hint: In the diagram given above since there is no frictional force between the ground and the three objects. The force which is applied will only be opposed by the objects and not by the frictional force of the ground. So, the object will move.

Complete step by step solution:
Here we apply the second law of Newton i.e.
$F = ma$;
Here:
F = Force;
m = Mass;
a = Acceleration
Here we would consider the force on the middle object ‘m’ which is in blue color. We have been given that the contact force between mass M and m is N and between m and M’ is N’ so the mass m has two horizontal forces one form M and another from M’. Here the two horizontal forces are acting opposite to each other.

Here the N force is between objects of Mass M and m and force N’ is between m and M’.
According to Newton’s second law the net force on the object of mass m would be:
${F_{Net}} = ma$;
Here the net force on the mass is:
${F_{Net}} = N - N'$;
Put the above value in the equation ${F_{Net}} = ma$:
$N - N' = ma$;
Since the objects are moving as there is no friction between the surface and the object $\therefore $ N>N’.

Final Answer: Option “B” is correct.

Note: Here we need to resolve the horizontal forces between the objects. Here we are considering the object ‘m’ because the other two masses ‘M and M’ are indirectly applying the force on each other through mass ‘m’. Resolve the forces on mass m and apply Newton’s second law. Since, the objects are moving the force N is greater than N’.