This question has statement `1` and statement `2` . Of the four choice given after the Statement , choose the one that best describe the two Statement .
If the spring `S_(1) `and `S_(2)` of force constant `k_(1)` and `k_(2)` respectively , are streached by the same force , it is found that more work is done on spring `S_(1)` then on spring `S_(2)`
Statement -1: If statement by the same answer work done on `S_(1)` work on `S_(1)` is more then `S_(2)`
Statement - 2 : `k_(1) ltk_(2)`

Options

A. Statement - 1 is ture , statement -2 is true, and statement-2 is correct explanation of statement -1.
B. Statement-1 if ture, statement-2 is true, but statement -2 is not a correct explanation of statement-1.
C. Statement-1 is true, but statement -2 is false.
D. Statement-1 is false, but statement-2 is true.

Answer

D

Explanation

Let `x_(1)` be extension produced in `S_(1)` and `x_(2)` be extension produced in `S_(2)`, when
two springs are stretched by the same force.
`:. F=K_(1)x_(1)=K_(2)x_(2)`
`W_(1)=Fx_(1)`
and `W_(2)=Fx_(2)`
As`W_(1) gt W_(2),Fx_(1) gt Fx_(2)` or `x_(1) gt x_(2)`
`:. K_(1) lt K_(2)`
Statement 2 is true.
When two springs are stretched by the same amount, `i.e., x_(1)=x_(2)=x`
`W_(1)=(1)/(2) K_(1)x^(2)`
As `K_(1) lt K_(2), W_(1) lt W_(2)`.
Statement 1 is false.