Question

Same spring is attached with $2 \,kg$, $3 \,kg$ and $1 \,kg$ blocks in three different cases as shown in figure. If $x_{1}, x_{2}$ and $x_{3}$ be the extensions in the spring in these cases then (Assume all the blocks to move with uniform acceleration)

• A. $x_{1}=0, x_{3}>\,x_{2}$
• B. $x_{2}>\,x_{1}>\, x_{3}$
• C. $x_{3}>\,x_{1}>\,x_{2}$
• D. $x_{1}>\,x_{2}>\,x_{3}$

Answer 1

Answer: (B)

If $m_{1}$ and $m_{2}$ are masses of blocks then tension $T$ in the string as well as spring are
$T=\frac{2m_{1}m_{2}}{m_{1}+m_{2}}g$
$T_{1}=2\,g$,
$T_{2}=2.4\,g$
and $T_{3}=1.33\,g$
$\therefore T_{2}>\,T_{1}>\,T_{3}$
or $x_{2}>\,x_{1}>\,x_{3}$
$t=\frac{v_{0}}{g}=\frac{(10/3)}{10}$
$=\frac{1}{3}\, sec$