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Question

If two springs S1 and S2 of force constants k1 and k2 respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2.

Statement-1: If stretched to the same extension, work done on S1, will be more than that on S2

Statement-2: k1<k2

Choose the correct option.
  1. Statement-1 is false, Statement-2 is true
  2. Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
  3. Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of statement-1.
  4. Statement-1 is true, Statement-2 is false


Solution

The correct option is A Statement-1 is false, Statement-2 is true
As given,
Both springs are stretched by same force
F=k1x1=k2x2
k1k2=x2x1     ...(1)
W1=12k1x21 and W2=12k2x22
W1 & W2 are work done on spring (1) & (2)
as given in question,W1>W2, W1W2>1
so, 12k1x2112k2x22>1  k1x1=k2x2
x1x2>1, k2k1>1  { eq (1)}
Therefore k2>k1, statement (2) is correct.
As, If x1=x2=x statement (1)
W1W2=12k1x212k2x2
W1W2=k1k2<1 {From statement (2)}

W1<W2 but in question (W1>W2).
Hence Statement 1 is false.
 

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