JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Elasticity & SHM

For an elastic string, tension is proportional to extension:
$T=k(\ell -{\ell }_0)$

where k is the spring constant and ℓ₀ is the original (natural) length.

Given two conditions:
$5=k(1.4-{\ell }_0)$ ... (1)
$7=k(1.56-{\ell }_0)$ ... (2)

Dividing equation (2) by equation (1):
$\frac{7}{5}=\frac{1.56-{\ell }_0}{1.4-{\ell }_0}$

$7(1.4-{\ell }_0)=5(1.56-{\ell }_0)$

$9.8-7{\ell }_0=7.8-5{\ell }_0$

$2{\ell }_0=2$

${\ell }_0=1$ m

Therefore, the original length is 1 m.