Question

Find the magnitude of acceleration (in ${\text{m/s}}^2$) of the system if all surfaces are smooth. $g=10{\text{m/s}}^2$.

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is B 3

Acceleration of the blocks are shown in the FBD

So, from the FBDs we have
$T_2-4g.sin{30}^{\circ }=4a$.........(i)
$5g-T_1=5a$...................(ii)
On solving (i) & (ii) we have
$T_2-T_1+3g=9a$............(iii)
Now, from the FBD of $1Kg$ mass
$T_1-T_2=a$...........(iv)

From eq (iii) & (iv) we have,
$3g=10a⟹a=\frac{30}{10}=3m/s^2$

Alternate:

Supporting force = $5g=5\times 10=50N$
Opposing force = $4g.sin{30}^{\circ }=2g=20N$
Magnitude of acceleration of the system is given by,
$a=\frac{\text{Supporting Force - Opposing Force}}{\text{Total mass}}$
$=\frac{5g-2g}{10}=3{\text{m/s}}^2$