JEE Main · 2012 · 29 Apr 2012 · Offline · Elasticity & SHM

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This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.

If two springs

S_{1}

and

S_{2}

of force constants

k_{1}

and

k_{2}

, respectively, are stretched by the same force, it is found that more work is done on spring

S_{1}

than on spring

S_{2}

.
Statement 1: If stretched by the same amount, work done on

S_{1}

will be more than that on

S_{2}

Statement 2:

k_{1} < k_{2}

(A)Statement 1 is false, Statement 2 is true✓ Correct
(B)Statement 1 is true, Statement 2 is false
(C)Statement 1 is true, Statement 2 is the correct explanation for statement 1
(D)Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1

Answer: (A)

Solution

Pulled by the same force, a spring stores

W = \frac{F ^{2}}{2 k}

, so more work is done on the softer spring; since here

W_{1} > W_{2}

, it follows that

k_{1} < k_{2}

, making the second statement true. Now test the first: if instead both springs are stretched by the same amount

x

, the work is

W = \frac{1}{2} k x^{2}

, and with

k_{1} < k_{2}

this gives

W_{1} < W_{2}

, not more. The first statement is therefore false while the second is true.

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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JEE Main · 2012 · 29 Apr 2012 · Offline · Elasticity & SHM

Solution

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