Assertion: Two springs of force constants k1 and k2 are stretched by the same force. If…
Physics · JEE Advanced · NTA Exams — Work, Energy and Power
Assertion: Two springs of force constants k1 and k2 are stretched by the same force. If k1 > k2, then work done in stretching the first spring (W1) is less than work done in stretching the second spring (W2).
Reason: F = k1x1 = k2x2
\(\text { ∴ }\) \(\frac{x_{1}}{x_{2}}=\frac{k_{2}}{k_{1}}\)
\[\frac{W_{1}}{W_{2}}=\frac{\frac{1}{2} k_{1} x_{1}^{2}}{\frac{1}{2} k_{2} x_{2}^{2}}=\frac{k_{1}}{k_{2}}\left(\frac{k_{2}}{k_{1}}\right)^{2}=\frac{k_{2}}{k_{1}}\]
As k1 > k2, W1 < W2
Reason: F = k1x1 = k2x2
\(\text { ∴ }\) \(\frac{x_{1}}{x_{2}}=\frac{k_{2}}{k_{1}}\)
\[\frac{W_{1}}{W_{2}}=\frac{\frac{1}{2} k_{1} x_{1}^{2}}{\frac{1}{2} k_{2} x_{2}^{2}}=\frac{k_{1}}{k_{2}}\left(\frac{k_{2}}{k_{1}}\right)^{2}=\frac{k_{2}}{k_{1}}\]
As k1 > k2, W1 < W2
- If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
- If both Assertion and Reason are true but Reason is not correct explanation of the Assertion.
- If Assertion is true but Reason is false.
- If Assertion is false but Reason is true.
Answer
(A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
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