Same spring is attached with 2 ~kg, 3 ~kg and 1 ~kg blocks in three...

Same spring is attached with

2 \mathrm{~kg}, 3 \mathrm{~kg}

and

1 \mathrm{~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 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,

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,

Options

A $x_1=0, x_3>x_2$
B $x_1>x_2>x_3$
C $x_3>x_2>x_1$
D $x_2>x_1>x_3$

Correct answer

D. $x_2>x_1>x_3$

Step-by-step solution

T_1, T_2, T_3

are the tensions in the strings in the three cases, we have

\begin{aligned} & T_1=\frac{2 m_1 m_2 g}{m_1+m_2}=\frac{2 \times 2 \times 2 g}{(2+2)}=2 g \\ & T_2=\frac{2 \times 3 \times 2 g}{(3+2)}=2.4 g \\ & T_3=\frac{2 \times 1 \times 2 g}{(1+2)}=1.33 g \\ & \text{ As } x \propto T \text{ and } T_2>T_1>T_3 \\ & \therefore \quad x_2>x_1>x_3\end{aligned}

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