An elastic spring under tension of 3 N has a length . Its length is under tension 2 N. For its length the value of tension will be ______ N.

Question

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]

Smart Achievers · Accepted Answer

(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)

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

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

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

Solution

Q.
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]

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Solution

Q. 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]

Ans. (5) k(a-x0)=3⇒a=3k+x0 ...(i) k(b-x0)=2⇒b=2k+x0 ...(ii) Now, 3a-2b=9k+3x0-4k-2x0=5k+x0 ⇒{(3a-2b)-x0}=5k ⇒k{(3a-2b)-x0}=5 ∴T=5N

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Q.
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]