Question

Two blocks of masses M = 5 kg and m = 3 kg are placed on a horizontal surface as shown in the figure. The coefficient of friction between the blocks is 0.5 and that between the block M and the horizontal surface is 0.7. What is the maximum horizontal force F that can be applied to block M so that both the blocks move together?

• A. 4 N
• B. 16 N
• C. 24 N
• D. 96 N

Answer 1

The correct option is D

96 N

The only horizontal force acting on mass m is the force of friction f.
$f=\mu mg=0.5\times 3\times 10=15N$
This force can produce an acceleration in block m given by $a=\frac{f}{m}=\frac{15}{3}=5m/s^2$
So, for the blocks to move together, they should have this common acceleration of $5m/s^2$.
Now, $F-f^{\prime }=(m+M)a\Rightarrow F-{\mu }^{\prime }(m+M)g=(m+M)a\Rightarrow F-0.7\times (3+5)\times 10=(3+5)\times 5\Rightarrow F-56=40\Rightarrow F=96N$
Hence, the correct choice is (d).