A massless spring gets elongated by amount under a tension of 5 N. Its elongation is under the tension of 7 N. For the elongation of (), the tension in the spring will be, [2025]

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Solution

Q.
A massless spring gets elongated by amount $x_{1}$ under a tension of 5 N. Its elongation is $x_{2}$ under the tension of 7 N. For the elongation of ( $5 x_{1} - 2 x_{2}$ ), the tension in the spring will be, [2025]

1 15 N

2 20 N

3 11 N

4 39 N

Ans.
(3)

$k x_{1} = 5 N \Rightarrow x_{1} = \frac{5}{k}$

$k x_{2} = 7 N \Rightarrow x_{2} = \frac{7}{k}$

Then $(5 x_{1} - 2 x_{2}) k = 5 \times 5 - 2 \times 7 = 11 N$ .

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