Question

When a certain force is applied on a string it extends by $0.01cm$. When the same force is applied on another string of same material, twice the length and double the diameter, then the extension in second string is

• A. 0.005 cm
• B. 0.02 cm
• C. 0.08 cm
• D. 0.04 cm

Answer 1

The correct option is A 0.005 cm

$△l=\frac{Fl}{\pi (\frac{d}{2}{)}^{2}Y}$

$0.01=\frac{Fl}{\pi (\frac{d}{2}{)}^{2}Y}$

$△l_1=\frac{F2l}{\pi 4(\frac{d}{2}{)}^{2}Y}$

$=\frac{1}{2}\frac{Fl}{\pi (\frac{d}{2}{)}^{2}Y}$ (also take the ratio in the next step)

$\frac{1}{2}\left(0.01\right)$

$=0.005cm$