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# Three blocks of masses ${{\text{m}}_{1}},{{\text{m}}_{2}}$ and ${{\text{m}}_{3}}$ are placed on a horizontal frictionless surface. A force of 40 N pulls the system. Then calculate the value of T if ${{\text{m}}_{1}}=10\text{ kg, }{{\text{m}}_{2}}=6\text{ kg, }{{\text{m}}_{3}}=4\text{ kg}$ (A) 40 N(B) 20 N(C) 10 N(D) 5 N

Last updated date: 13th Jun 2024
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Hint: We know that tension T can be formed by using the formula
T=ma
Now, at the point A tension T is due to sum of masses ${{\text{m}}_{2}}$ and ${{\text{m}}_{3}}$
So,
$\text{T=}\left( {{\text{m}}_{2}}+{{\text{m}}_{3}} \right)\text{a}$
Using this formula, tension T can be found.

Complete step by step solution
We know that F=ma
Here we have 3 masses, ${{\text{m}}_{1}}=10\text{ kg, }{{\text{m}}_{2}}=6\text{ kg, }{{\text{m}}_{3}}=4\text{ kg}$
So F= $\left( {{\text{m}}_{1}}+{{\text{m}}_{2}}+{{\text{m}}_{3}} \right)\text{a}$
$=\left( 10+6+4 \right)\text{a}$
F=20 a
F=40 N…… (Given)
So, 40=20a
a=2
Now tension T is given as:
T= $\left( {{\text{m}}_{2}}+{{\text{m}}_{3}} \right)\text{a}$
\begin{align} & =\left( 6+4 \right)\times 2 \\ & =10\times 2 \\ \end{align}
T=20 N
So, the correct option is (B).

Note
Tension is described as the pulling force transmitted axially by means of a string, cable, chain or 1-D objects. Tension never applies on its own. It has to be put on a system and it is always a pulling force.