Question

In the given figure the coefficient of friction between 4 kg and 5 kg blocks is 0.2 and between 5 kg block and ground is 0.1 respectively. Choose the correct statements.

• A. Minimum force needed to cause system to move is 17 N
• B. When force is 4N static friction at all surfaces is 4N to keep system at rest
• C. Maximum acceleration of 4 kg block is $2m/s^2$
• D. Slipping between 4 kg and 5 kg blocks start when F is > 17N

Answer 1

The correct option is C Maximum acceleration of 4 kg block is $2m/s^2$

friction force by floor can be maximum $\mu Mg=0.1\times (4+5)\times 10=9N$
so any force greater than 9 N will move system. so,(A) is incorrect.
when force is 4 N there will be 4N friction between ground and larger block but nothing between two blocks as they are not tending to move relatively.so, (B) is incorrect.
There is no external force on 4 Kg block except friction so maximum force can be $\mu mg$ and maximum acceleration $\mu g=0.2\times 10=2m/s^2$. so,(C) is correct.

slipping between two blocks start when smaller block has reached its maximum acceleration that is 2. so acceleration of system will also be 2, so total force has to be atleast $=2\times (5+4)+f_r=18+\mu (5+4)10=18+9=27N$ . so, (D) is incorrect