Question

If the system shown in the figure is at rest initially, find the common acceleration of the two block system?
(Take $g=10m/s^2$)

• A. $2m/s^2,\text{in +ve x-direction}$
• B. $2m/s^2,\text{in -ve x-direction}$
• C. $3m/s^2,\text{in -ve x-direction}$
• D. $3m/s^2,\text{in +ve x-direction}$

Answer 1

The correct option is B $2m/s^2,\text{in -ve x-direction}$

The FBDs of the blocks are as shown


From the FBDs we have
$N_1=10g=100\text{N}$
$N_2=N_1+20g=100+200=300\text{N}$
$f_{\text{1 max}}=\mu N_1=1\times 100=100\text{N}$
$f_{\text{2 max}}=\mu N_2=0$

Now, assuming that the blocks moves together in $-ve$ x-direction with common acceleration $a_c$
$\therefore$ common acceleration $a_c=\frac{60}{m_A+m_B}=\frac{60}{30}=2m/s^2$

Again, from the FBD of block $B$ we have
$f=m_B{a}_c=20\times 2=40\text{N}$
Since, $40\text{N}<100\text{N}$ i.e. $f<f_{\text{max}}$, means our assumption is right.

Hence, both the block will move together in $-ve$ x-direction with common acceleration $a_c=2m/s^2$