Question

In the figure the coefficient of friction between the floor and the body $B$ is $0.1$. The coefficient of friction between the bodies $B$ and $A$ is $0.2$. A force $F$ is applied as shown on $B$. The mass of $A$ is $m/2$ and $B$ is $m$. Which of the following statements are true?

• A. The bodies will move together if $F=0.25mg$
• B. The body $A$ will slip with respect to $B$ if $F=0.5mg$
• C. The bodies will move together if $F=0.5mg$
• D. The bodies will be at rest if $F=0.1mg$

Answer 1

The correct option is A The bodies will move together if $F=0.25mg$

To here first we have to find first frictional forces on each surface and accordingly we will decide maximum force. The friction force always have tendency to oppose the motion. In the given diagram, let the frictional force between floor and block B is (f1) and frictional force between block B and A is (f2) will be as shown. ‘ Let A and B are moving together

Then F = 0.25 mg

From above equations