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JEE Main
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Physics
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Experimental Physics

JEE Main · Physics · Experimental Physics

If a tuning fork of frequency ( f _ 0 )340Hz and tolerance ± 1 % is...

If a tuning fork of frequency (f0)340Hz( {f}_{0} )340Hz and tolerance ±1\pm 1 % is used in the resonance column method for determining the speed of sound. If the first and the second resonance are measured at l1=24.0cm{l }_{1} = 2 4.0 cm and l2=74.70cm{l }_{2} = \text{74.70} cm, then the permissible error in speed of sound is

Options

  1. A1.21 . 2 %
  2. B1.81 . 8 %
  3. C11 %
  4. D0.80 . 8 %

Correct answer

A. 1.21 . 2 %

Step-by-step solution

V=2f0(l2−l1)<br/><br/>letl2−l1=\text{V} = {2 f}_{0} \left({l}_{2} - {l}_{1}\right)<br/><br/>\text{let} {l}_{2} - {l}_{1} =x<br/><br/><br/><br/>{l}_{1} = \left(\text{24.0} \mathop{+}_{¯} \text{0.1}\right) \text{cm}

l2=(74.70+¯0.01)cm<br/><br/>{l}_{2} = \left(\text{74.70} \mathop{+}_{¯} \text{0.01}\right) \text{cm}<br/><br/>{l}_{2} - {l}_{1} = \left(\text{50.70} \mathop{+}_{¯} \text{0.11}\right) \text{cm}

\dfrac{\Delta x}{x} = \left(\dfrac{\text{0.11}}{\text{50.70}}\right)

\Deltaxx\text{%} = \dfrac{\text{0.11}}{\text{50.70}} \times \text{100}

=\text{0.22%}

\Delta \text{V} \text{%} = \Delta {f}_{0} \text{%} + \Deltaxx\text{%}

=\text{1.22} \text{%}

=\text{1.2} \text{%}
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