Question

When a mass of $8\text{kg}$ is suspended from a string, its length is $l_1$. If a mass $10\text{kg}$ is suspended, its length is $l_2$. Length, when a mass of $16\text{kg}$ is suspended from it, is given by

• A. $2l_2-l_1$
• B. $2l_2+l_1$
• C. $4l_2+3l_1$
• D. $4l_2-3l_1$

Answer 1

The correct option is D $4l_2-3l_1$

$\Delta l_1=\frac{F_{1}l}{AY}$
$\Rightarrow l+\Delta l_1=l(\frac{F_1}{AY}+1)=l(\frac{8g}{AY}+1)$
again, $\Delta l_2=\frac{F_{2}l}{AY}$
$\Rightarrow l+\Delta l_2=l(\frac{F_2}{AY}+1)=l(\frac{10g}{AY}+1)$
again, $\Delta l_3=\frac{F_{3}l}{AY}$
$\Rightarrow l+\Delta l_3=l(\frac{F_3}{AY}+1)=l(\frac{16g}{AY}+1)$
$\therefore l_3=4l_2-3l_1$

Why this question? Tip: Some simple questions based on the direct application of important results is asked even in JEE Advanced. This one is not be missed!