Laws of Motion

JEE Main level, single correct, medium

119 of 210

Question 119 of 210

If two similar springs each of spring constant K1{K}_{1} are joined in series, the new spring constant and time period would be changed by a factor:

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Answer: (D) 12,2\dfrac{1}{2},\sqrt{2}

1keq=1k1+1k2\dfrac{1}{{k}_{eq}}=\dfrac{1}{{k}_{1}}+\dfrac{1}{{k}_{2}}
1keq=1k+1k⇒keq=k2\dfrac{1}{{k}_{eq}}=\dfrac{1}{k}+\dfrac{1}{k}\Rightarrow {k}_{eq}=\dfrac{k}{2}
k′=k2{k}^{'}=\dfrac{k}{2}
T=2πMkT=2\pi \sqrt{\dfrac{M}{k}}
T′=2πMk′{T}^{'}=2\pi \sqrt{\dfrac{M}{{k}^{'}}}
⇒T′=2πMk×2\Rightarrow {T}^{'}=2\pi \sqrt{\dfrac{M}{k}}\times \sqrt{2}
T′=2T{T}^{'}=\sqrt{2}T

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