  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.Statement-1 is false, Statement-2 is trueStatement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of statement-1.Statement-1 is true, Statement-2 is false

Solution

## The correct option is A Statement-1 is false, Statement-2 is trueAs 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.  Suggest corrections   