Question

Block $B$ rests on a smooth surface. If the coefficient of static friction between $A$ and $B$ is $\mu =0.4$. Determine the acceleration of each block, if weight of lower block is $250N$ and $F=30N$.

• A. $0.85{\text{ms}}^{-2}$
• B. $1{\text{ms}}^{-2}$
• C. $1.65{\text{ms}}^{-2}$
• D. $2{\text{ms}}^{-2}$

Answer 1

The correct option is A $0.85{\text{ms}}^{-2}$


Limiting friction between A and B $f_L=\mu N=0.4\times 100=40N$
(a) Both the blocks will have a tendency to move together with same acceleration (say $a$). So, the free body diagram is as shown.
Equations of motion are,
$30-f=10\times a....\left(i\right)$
$f=25\times a......\left(ii\right)$
solving these two equations, we get
$a=0.857{\text{m/s}}^{2}andf=21.42N$
As this force is less than $f_L$, both the blocks will moves together with same acceleration,
$a_A=a_B=0.857{\text{m/s}}^2$