Question

In the figure shown, find the acceleration of the block $B$. Assume all surfaces to be smooth.

• A. $a=\frac{3F}{20m}{\text{m/s}}^2$
• B. $a=\frac{3F}{21m}{\text{m/s}}^2$
• C. $a=\frac{2F}{21m}{\text{m/s}}^2$
• D. $a=\frac{3F}{18m}{\text{m/s}}^2$

Answer 1

The correct option is B $a=\frac{3F}{21m}{\text{m/s}}^2$

Direction of acceleration of blocks are shown in below figure.
From the constrained condition and using the method of intercept we have
${\stackrel{..}{L}}_1+{\stackrel{..}{L}}_2+{\stackrel{..}{L}}_3=0$
$\Rightarrow -b+a+a-b-b-c=0$
$\Rightarrow 2a=3b+c$............(1)


From the FBDs we have


$F-2T=2ma\Rightarrow a=(\frac{F}{2m}-\frac{T}{m})$ ... (2)
$T=mc\Rightarrow c=\frac{T}{m}$ ... (3)
$3T=4mb\Rightarrow b=\frac{3T}{4m}$ ... (4)

On putting the value of $a$, $b$ and $c$ in eq (1) we get
$b=\frac{3F}{21m}{\text{m/s}}^2$
Thus, the acceleration of the block $B$ is $b=\frac{3F}{21m}m/s^2$