Question

Same spring is attached with $2kg,3kg$ and $1kg$ 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. $x_1=0,x_3>x_2$
• B. $x_1>x_2>x_3$
• C. $x_3>x_2>x_1$
• D. $x_2>x_1>x_3$

Answer 1

The correct option is D $x_2>x_1>x_3$

If $T_1,T_2,T_3$ are the tensions in the strings in the three cases, we have

$T_1=\frac{2m_1{m}_{2}g}{m_1+m_2}=\frac{2\times 2\times 2g}{(2+2)}=2g$

$T_2=\frac{2\times 3\times 2g}{(3+2)}=2.4g$

$T_3=\frac{2\times 1\times 2g}{(1+2)}=1.33g$

As $x\propto T$ and $T_2>T_1>T_3$
$\therefore x_2>x_1>x_3$.