The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N. the length of the string is 1.56 m. The original length of the string is ______ m. [2025]

Question

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N. the length of the string is 1.56 m. The original length of the string is ______ m. [2025]

Smart Achievers · Accepted Answer

(1)

$T = K (l - l_{0})$

$\Rightarrow 5 = K (1.4 - l_{0})$

$\Rightarrow 7 = K (1.56 - l_{0})$

$\Rightarrow \frac{5}{1.4 - l_{0}} = \frac{7}{1.56 - l_{0}}$

$∴ l_{0} = 1 m$

Solution

Q.
The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N. the length of the string is 1.56 m. The original length of the string is ______ m. [2025]

Ans.
(1)

$T = K (l - l_{0})$

$\Rightarrow 5 = K (1.4 - l_{0})$

$\Rightarrow 7 = K (1.56 - l_{0})$

$\Rightarrow \frac{5}{1.4 - l_{0}} = \frac{7}{1.56 - l_{0}}$

$∴ l_{0} = 1 m$

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Solution

Q. The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N. the length of the string is 1.56 m. The original length of the string is ______ m. [2025]

Ans. (1) T=K(l–l0) ⇒ 5=K(1.4–l0) ⇒ 7=K(1.56–l0) ⇒ 51.4–l0=71.56–l0 ∴ l0=1 m

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Q.
The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N. the length of the string is 1.56 m. The original length of the string is ______ m. [2025]

Ans.
(1)

$T = K (l - l_{0})$

$\Rightarrow 5 = K (1.4 - l_{0})$

$\Rightarrow 7 = K (1.56 - l_{0})$

$\Rightarrow \frac{5}{1.4 - l_{0}} = \frac{7}{1.56 - l_{0}}$

$∴ l_{0} = 1 m$