Question

Find the acceleration of block $A$ and $B$? Take $g=10m/s^2$

• A. $a_A=1{\text{m/s}}^2,a_B=1{\text{m/s}}^2$
• B. $a_A=1{\text{m/s}}^2,a_B=2{\text{m/s}}^2$
• C. $a_A=1{\text{m/s}}^2,a_B=0{\text{m/s}}^2$
• D. $a_A=0{\text{m/s}}^2,a_B=1{\text{m/s}}^2$

Answer 1

The correct option is C $a_A=1{\text{m/s}}^2,a_B=0{\text{m/s}}^2$

The FBDs are as shown below
Given, applied external force $F=30N$


From the FBDs we have
$N_1=5g=50\text{N}$
$f_{1\text{max}}=\mu N_1=0.5\times 50=25\text{N}$
$N_2=N_1+10g=50+100=150\text{N}$
$f_{2\text{max}}=0.5\times 150=75\text{N}$

Since, $F<75\text{N},10\text{kg}$ block will not move.
For $5\text{kg}$ block, $F>f_{\text{1 max}}$,
Hence, it will accelerate at
$a_A=\frac{F-f_{\text{1 max}}}{m_A}=\frac{30-25}{5}=1{\text{m/s}}^2$