Question

Same spring is attached with 2 kg, 3 kg and 1 kg blocks in three different cases as shown in figure. If $x_1,x_2,x_3$ be the extensions in the spring in the three cases, then

• A. x₁= 0, x₃ > x₂
• B. x₁ > x₂ > x₃
• C. x₃ > x₂ > x₁
• D. x₂ > x₁ > x₃

Answer 1

Answer: (D)

If $T_1$, $T_2$, $T_3$ are the tensions in the strings in the three cases, we have
$T_1=\frac{2m_1{m}_{2}g}{m_1+m_2}=\frac{2\times 2\times 2g}{\left(2+2\right)}=2g$
$T_2=\frac{2\times 3\times 2g}{\left(3+2\right)}=2.4g$
$T_3=\frac{2\times 1\times 2g}{\left(1+2\right)}=1.33g$
As x $\propto$ T and $T_2>T_1>T_3$
$\therefore x_2>x_1>x_3$