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Question: Three blocks are connected as shown in the figure, on a horizontal frictionless table and pulled to ...

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 M1=10 kg{M_1} = 10\,kg , M2=20 kg{M_2} = 20\,kg and M3=30 kg{M_3} = 30\,kg then the value of T2{T_2} :

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

Explanation

Solution

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−2a\,m\,{s^{ - 2}} and net force acting on system is F. According to Newton’s second law of motion:
F=maF = ma
Where,
F=F = net force on system
a=a = net acceleration
m=m = net mass of system
External force on the system is 60N60N which forms the net force on the system.
Total mass of system =30+20+10=60kg= 30 + 20 + 10 = 60kg
Putting these values in Newton’s second law of motion:
60=60×a60 = 60 \times a
a=1 m s−2a = 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 M3{M_3} ,
Net force on block F3=F−T2  N{F_3} = F - {T_2}\,\,N
Mass M3=30 kg{M_3} = 30\,kg
Acceleration of block a=1 m s−2a = 1\,m\,{s^{ - 2}}
Applying Newton’s law of motion we will get,
F−T2=M3×aF - {T_2} = {M_3} \times a
Putting values in the above equation:
60−T2=30×160 - {T_2} = 30 \times 1
Evaluating the above equation will give:
⇒  T2=30 N\Rightarrow \,\,{T_2} = 30\,N
∴\therefore The value of T2T_2 is 30N30N. 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 T1T_1 value, we can use the net force as
T1=M1×aT_1= M_1 \times a w.r.t M1M_1
and we can also find T2T_2 from T1T_1 value w.r.t. M2M_2
T2−T1=M2×aT_2 - T_1 = M_2 \times a