Three blocks A, B and C are pulled on a horizontal smooth surface...

Three blocks $A, B$ and $C$ are pulled on a horizontal smooth surface by a force of $80N$ as shown in figure. The tensions ${T}_{1}\text{and}{T}_{2}$ in the string are respectively:

Options

A $40N, 64N$
B $60N, 80N$
C $88N, 96N$
D $80N, 100N$

Correct answer

A. $40N, 64N$

Step-by-step solution

Since, the length of the string will remain same. Hence, all blocks will have the same acceleration.
${a}_{A} = {a}_{B} = {a}_{C} = \dfrac{F}{5 + 3 + 2} = \dfrac{80}{10} = 8m{s}^{- 2}$
Therefore, ${T}_{1} = 5 \times 8 = 40N$ .
Now,
${T}_{2} - {T}_{1} = 3 \times 8 ⇒ {T}_{2} = 64N$

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