Question

Three blocks are connected as shown in the figure, on a horizontal frictionless table and pulled to the right with a force of 60N. If ${M_1} = 10\,kg$ , ${M_2} = 20\,kg$ and ${M_3} = 30\,kg$ then the value of ${T_2}$ :

A) 90N
B) 45N
C) 60N
D) 30N

Answer 1

Hint: By drawing a free body diagram of the blocks we can obtain the relation between force and tension. As the acting force is bringing about a net movement in the system, we must let a net acceleration of the system. Remember with this net acceleration only all the blocks will move.

Complete step by step answer:
We must first draw a free body diagram of all blocks to clearly understand the forces acting on all the blocks:

Above we can clearly see the direction and the forces on each block.
Now let net acceleration of the system be $a\,m\,{s^{ - 2}}$ and net force acting on system is F. According to Newton’s second law of motion:
$F = ma$
Where,
$F =$ net force on system
$a =$ net acceleration
$m = $net mass of system
External force on the system is $60N$ which forms the net force on the system.
Total mass of system $= 30 + 20 + 10 = 60kg$
Putting these values in Newton’s second law of motion:
$60 = 60 \times a$
$a = 1\,m\,{s^{ - 2}}$
Net acceleration on a system is the acceleration of all blocks. The movement of the system will be in the direction of external force. Applying Newton’s second law of motion on blocks separately we will get,
On block ${M_3}$ ,
Net force on block ${F_3} = F - {T_2}\,\,N$
Mass ${M_3} = 30\,kg$
Acceleration of block $a = 1\,m\,{s^{ - 2}}$
Applying Newton’s law of motion we will get,
$F - {T_2} = {M_3} \times a$
Putting values in the above equation:
$60 - {T_2} = 30 \times 1$
Evaluating the above equation will give:
$ \Rightarrow \,\,{T_2} = 30\,N$
$\therefore $ The value of $T_2$ is $30N$. So, option (D) is correct.

Note:
Tension is the internal force generated due to the action of external force. As it is a developed force in strings, it never takes part in the net force of the system. Net force of the system is contributed by external forces only.
If we want to find the $T_1$ value, we can use the net force as
$T_1= M_1 \times a$ w.r.t $M_1$
and we can also find $T_2$ from $T_1$ value w.r.t. $M_2$
$T_2 - T_1 = M_2 \times a$