Question

2
The length of an elastic string is X m when the tension is 8 N, and Ym when the tension is 10 N. The length
in metres when the tension is 18 N is
(1) 4X-5Y
(25Y- 4x
(3) 9X-47
(4) 4Y- 9x​

Answer 1

Answer:

5y - 4x

Explanation:

Solution

Let, original length of the spring is L metre and, Y = A.lF.L

Now, when F = 8N, and l = (x - l)m then, Y=A.(x−L)8.L⟶(I)

and when F=10N, and l = (y - l)m then, y=A.(y−L)10.Lm⟶(II)

From equation (I) and (II) we get,

A(x−L)8L=A(y−L)10L

or,  8(y−L)=10(x−L)

or,    4y−4L=5x−5L

or,                L=5x−4y

When, F=18N,

Let, length of the wire will be Z metre.

∴Y=A.(Z−L)18.L⟶(III)

From equation (I) and (III) we get,

A(x−L)8L=A(Z−L)18L

or,  9(x−L)=4(Z−L)

or,  4Z=9x−9L+4L

            =9x−5L

            =9x−25x+20y    [putting value of L]

or,  Z=5y−