Question

Three blocks of masses $2 kg , 3 kg$ and $5 kg$ are connected to each other with light string and are then placed on a smooth frictionless surface. The system is pulled with force F from side of the lighter mass so that it moves with an acceleration of $1 ms ^{-2}, T _{1}$ and $T _{2}$ denote the tension in the other strings. The value of $F$ is

• A. $30 N$
• B. $20 N$
• C. $10 N$
• D. $40 N$

Answer 1

Answer: (C)

Equations of motions are
for $2 kg$. block, $F - T _{1}=2 a\ldots $(i)
for $3 kg$ block, $T _{1}- T _{2}=3 a \ldots$ (ii)
For $5 kg$ block
$T _{2}=5 a$(iii)
putting the value of $T _{2}$ in eq (ii)
$\therefore T _{1}-5 a =3 a \Rightarrow T _{1}=8 a$ [Putting in eq (i)]
$F-8 a=2 a \Rightarrow $
$F=10 N \quad\left( a =1 m / s ^{2}\right)$