SATHEE: Gravitation Question 223

Gravitation Question 223

Question: The length of an elastic string is $[a]$ metre when the longitudinal tension is 4 N and $[b]$ metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

Options:

A) $[a - b]$

B) $[5 b - 4 a]$

C) $[2 a - \frac{1}{4} a]$

D) $[4 a - 3 b]$

Show Answer

Answer:

Correct Answer: B

Solution:

Let L be the original length of the wire and K be the force constant of wire. Final length = initial length + Elongation $[L^{'} = L + \frac{F}{K}]$ For first condition $[a = L + \frac{4}{K}]$ (i) For second condition $[b = L + \frac{5}{K}]$ (ii) By solving equations (i) and (ii), we get $[L = 5 a - 4 b]$ and $[K = \frac{1}{b - a}]$ Now when the longitudinal tension is 9 N, length of the string $[= L + \frac{9}{K} = 5 a - 4 b + 9 (b - a) - 5 b - 4 a .]$

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Gravitation Question 223

Question: The length of an elastic string is [a] metre when the longitudinal tension is 4 N and [b] metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

Options:

Answer:

Solution:

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Question: The length of an elastic string is $[a]$ metre when the longitudinal tension is 4 N and $[b]$ metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is