A: A thread of length L is streatched by a force of 5N, its length increases by a and stretched by force of 6N its length increases by b, now if it is stretched by force of 11 N its length increases by `(a + b -L).`
R: Increasing the length of elastic thread is proportional to its initial length.

Options

A. Both are true and the reason is the correct explanation of the assertion.
B. Both are true but the reason is not correct explanation of the assertion.
C. Assertion is true, but the reason is false.
D. Both assertion and reason are false.

Answer

D

Explanation

If initial length is L and increase in length l due to force F then in `l = (FL)/(AY), (L)/(AY)=C`
`l = FC`
`therefore ` For first case ` a = L +l`
`therefore a = L + FC = L + 5 C " "…(1)`
`therefore b = L + F.C = L + 6C" "…(2)`
For second case,
`therefore b -a = L + 6C -L-5C`
`therefore b -a =C`
If increase in length is x due to force 11N then,
`x = L +11C" "[F=11x]...(3)`
From equation (1) and (2),
`C = (a -L)/(5) and C = (b-L)/(6)`
`therefore (a-L)/(5) = (b-L)/(6)`
`therefore 6a - 6L = 5-5L`
`therefore 6a 05b =L" "...(4)`
Putting value of equation (4) in equation (3),
`x = 6a - 5b + 11( b-a) [because C = b -a]`
`=6a - 5b +11b -11a`
`x = 6b -5a`
`therefore` Assertion is false and reason in true.