Question

Three masses of $1kg,6kg$ and $3kg$ are connected to each other with massless strings and are placed on a table as shown in figure.
If $g=10m{s}^{-2}$, the acceleration with which the system is moving is:

• A. $6m{s}^{-2}$
• B. $2m{s}^{-2}$
• C. $1m{s}^{-2}$
• D. $4m{s}^{-2}$

Answer 1

The correct option is B $2m{s}^{-2}$

Let the acceleration be 'a' and masses,

$m_1=1kg$, $m_2=6kg$ and $m_3=3kg$

Then ,

On writing force balance equation for $m_3$:

$m_{3}a=m_{3}g-T_2$ ..........(1)

Similarly for $m_2$:

$m_{2}a=T_1-T_2$...............(2)

And finally for $m_1$:

$m_{1}a=T_1-m_{1}g$...........(3)

Now, from equation (1),(2) and (3), we can write:

$(m_1+m_2+m_3)a=m_{3}g-m_{1}g$

On substituting the values of masses and $g$:

$⟹10a=2\times 10$

Hence,

$⟹$ Acceleration of the system, $a=2m{s}^{-2}$

So, the correct option is $\left(B\right)$