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Question

The length of an elastic string is x metre when the tension is 8 N. Its length is y metre when the tension is 10 N. What will be its length, when the tension is 18 N?

A
2x+y
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B
5y4x
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C
7y5x
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D
7y+5x
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Solution

The correct option is B 5y4x
Let, original length of the spring is L metre and, Y = F.LA.l
Now, when F = 8N, and l = (x - l)m then, Y=8.LA.(xL)(I)
and when F=10N, and l = (y - l)m then, y=10.LA.(yL)m(II)
From equation (I) and (II) we get,
8LA(xL)=10LA(yL)
or, 8(yL)=10(xL)
or, 4y4L=5x5L
or, L=5x4y
When, F=18N,
Let, length of the wire will be Z metre.
Y=18.LA.(ZL)(III)
From equation (I) and (III) we get,
8LA(xL)=18LA(ZL)
or, 9(xL)=4(ZL)
or, 4Z=9x9L+4L
=9x5L
=9x25x+20y [putting value of L]
or, Z=5y4x



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