Spring Force and Combination of Springs questions | Spring Force and Combination of Springs jee questions

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Q 1 :

An elastic spring under tension of 3 N has a length $a$ . Its length is $b$ under tension 2 N. For its length $(3 a - 2 b),$ the value of tension will be ______ N. [2024]

(5) $k (a - x_{0}) = 3 \Rightarrow a = \frac{3}{k} + x_{0}$ ...(i)

$k (b - x_{0}) = 2 \Rightarrow b = \frac{2}{k} + x_{0}$ ...(ii)

$Now, 3 a - 2 b = \frac{9}{k} + 3 x_{0} - \frac{4}{k} - 2 x_{0} = \frac{5}{k} + x_{0}$

$\Rightarrow {(3 a - 2 b) - x_{0}} = \frac{5}{k}$

$\Rightarrow k {(3 a - 2 b) - x_{0}} = 5$ $∴ T = 5 N$

Q 2 :

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]

15 N
20 N
11 N
39 N

(3)

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

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

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

Q 3 :

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]

(1)

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

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

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

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

$∴ l_{0} = 1 m$

Q 4 :

Find the ratio of the extension in upper spring to lower spring.

$\frac{m_{1} k_{1}}{m_{2} k_{2}}$
$\frac{m_{2} k_{1}}{m_{1} k_{2}}$
$\frac{(m_{1} + m_{2}) k_{2}}{m_{1} k_{1}}$
$\frac{(m_{1} + m_{2}) k_{2}}{m_{2} k_{1}}$

(4)

$k_{1} x_{1} = k_{2} x_{2} + m_{1} g; k_{2} x_{2} = m_{2} g$

$x_{1} = \frac{k_{2}}{k_{1}} [\frac{m_{2} g}{k_{2}}] + \frac{m_{1} g}{k_{1}}$

$x_{2} = \frac{m_{2} g}{k_{2}}$

$x_{1} = \frac{(m_{1} + m_{2}) g}{k_{1}}$

$\frac{x_{1}}{x_{2}} = \frac{(m_{1} + m_{2}) k_{2}}{k_{1} m_{2}}$

Topic Question Set

Q 1 :

An elastic spring under tension of 3 N has a length $a$ . Its length is $b$ under tension 2 N. For its length $(3 a - 2 b),$ the value of tension will be ______ N. [2024]

Q 2 :

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]

Q 3 :

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]

Q 4 :

Find the ratio of the extension in upper spring to lower spring.

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Topic Question Set

Q 1 : An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a-2b), the value of tension will be ______ N. [2024]

Q 2 : A massless spring gets elongated by amount x1 under a tension of 5 N. Its elongation is x2 under the tension of 7 N. For the elongation of (5x1–2x2), the tension in the spring will be, [2025]

Q 3 : 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]

Q 4 : Find the ratio of the extension in upper spring to lower spring.

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Q 1 :

An elastic spring under tension of 3 N has a length $a$ . Its length is $b$ under tension 2 N. For its length $(3 a - 2 b),$ the value of tension will be ______ N. [2024]

Q 2 :

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]

Q 3 :

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]

Q 4 :

Find the ratio of the extension in upper spring to lower spring.