Question

The tension in the string connected between the blocks is? (the surface is smooth)

1- \[\dfrac{80}{3}N\]
2- \[\dfrac{40}{3}N\]
3- \[\dfrac{50}{7}N\]
4- 26 N

Answer 1

Hint: We can see both the blocks are attached by a single rope, so there will be one common tension, T in the string.
We can make use of Newton’s second law to arrive at a meaningful answer here. Here the tension is a kind of force and it always acts towards the point of impact.

Complete step by step answer:
Let the tension in the string be T. Now the force acting towards the right is greater than the force acting towards left, so the system will move in the right direction with a common acceleration and let it be a.
There are two forces acting each on the two blocks and they are connected by a single rope. For the body of mass 4 kg: \[20-T=4a\] ------(1)
For the body of mass 2 kg: \[T-10=2a\] ------(2)
Solving eq (1) and (2) we get,
\[\begin{align}
  & 10=6a \\
 & \Rightarrow a=\dfrac{5}{3}m/{{s}^{2}} \\
\end{align}\]
Now to find the value of tension, we substitute the value of acceleration in eq (1), we get,
\[T=10+\dfrac{10}{3}=\dfrac{40}{3}N\]
Thus, the value of tension is \[\dfrac{40}{3}N\]

So, the correct answer is “Option 2”.

Note:
Remember force is a vector quantity and so its direction is also to be taken into account. Such problems can be briskly solved using Newton’s equations of motions. We have to add all the forces acting on the system, since force is a vector quantity, we have to take into account the direction also.