Question

In the figure shown, find the velocity of the $3kg$ mass after $10s$ if the system is released from rest at $t=0$. (Take $g=10m/s^2$)

• A. $30m/s$
• B. $40m/s$
• C. $50m/s$
• D. $70m/s$

Answer 1

The correct option is B $40m/s$

The FBD of the blocks are shown in the below figure

So, from the FBD we have
$7g-T=7a$......(i)
$T-3g=3a$.......(ii)
From the eq (i) & (ii), we get
$a=\frac{4g}{10}=4m/s^2$
From equation of motion we have,
$v=u+at$
$\Rightarrow v=0+4\times 10=40m/s$

OR

$a=\frac{\text{(Supporting force - opposing Force)}}{\text{Total mass}}$
$=\frac{7g-3g}{10}=4m/s^2$
From equation of motion we have,
$v=u+at$
$\Rightarrow v=0+4\times 10=40m/s$