First slide

Elastic Modulie

Question

The length of an elastic string is a metre when the tension is 4 N and b metre when the tension is 5 N.
The length, (in metre), when the tension is 9 N, is

Moderate

A

(a + b)
B

(4b $-$ 5a)
C

(5b $-$ 4a)
D

(9b $-$ 9a)

Solution

Let l be the natural length and k $(= \frac{Y A}{l})$ be the force
constant of wire. Then,
$a = l + \frac{4}{k}$ $\dots (i) (∵ F = k Δ l or Δ l = \frac{F}{k})$
and $b = l + \frac{5}{k}$ …(ii)
On solving Eqs. (i) and (ii), we get
$or \frac{1}{k} = (b - a) and l = (5 a - 4 b)$
Now, when T = 9N
$l' = l + \frac{9}{k} = (5 a - 4 b) + 9 (b - a) = (5 b - 4 a)$

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