Question

A system of two blocks of masses $m=2kg$ and $M=8kg$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $\mathrm{0.5.}$ The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be

• A. $9.8N$
• B. $39.2N$
• C. $49N$
• D. $78.4N$

Answer 1

The correct option is C $49N$


For $2kg$ block:
$a_{\text{max}}=\mu g$
$a_{max}=0.5\times 9.8=4.9m/s^2$
(this is the common acceleration of both the blocks)
Also:
$F_{\text{max}}=(M+m)a_{max}$
$\therefore F_{\text{max}}=(8+2)\times 4.9=49N$