First slide

Elastic behaviour of solids

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

Moderate

A

$a - b$
B

$5 b - 4 a$
C

$2 b - \frac{1}{4} a$
D

$4 a - 3 b$

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
$= L + \frac{9}{K} = 5 a - 4 b + 9 (b - a) = 5 b - 4 a$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App