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Oscillations question

2000 · Q161
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Oscillations question

2000 · Q161

NEETPhysicsOscillationsMCQ+4 / −1
Two masses MMMA and MMMB are hung from two strings of length lllA and lllB respectively. They are executing SHM with frequency relation fffA = 2fffB, then relation
  1. A
    lA=lB4{l_A} = {{{l_B}} \over 4}lA​=4lB​​ does not depend on mass
  2. B
    lA=4lB{l_A} = 4{l_B}lA​=4lB​, does not depend on mass
  3. C
    lA=2lB{l_A} = 2{l_B}lA​=2lB​ and MA=2MB{M_A} = 2{M_B}MA​=2MB​
  4. D
    lA=lB2{l_A} = {{{l_B}} \over 2}lA​=2lB​​ and MA=MB2{M_A} = {{{M_B}} \over 2}MA​=2MB​​.
View written solutionFree

Correct answer: A

fA=2fB{f_A} = 2{f_B}fA​=2fB​

⇒12πglA=2×12πglB\Rightarrow {1 \over {2\pi }}\sqrt {{g \over {{l_A}}}} = 2 \times {1 \over {2\pi }}\sqrt {{g \over {{l_B}}}}⇒2π1​lA​g​​=2×2π1​lB​g​​

⇒llA=4×llB \Rightarrow {l \over {{l_A}}} = 4 \times {l \over {{l_B}}}⇒lA​l​=4×lB​l​

⇒lA=lB4 \Rightarrow {l_A} = {{{l_B}} \over 4}⇒lA​=4lB​​ , which does not depend on mass.

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