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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
A mass $M$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively as shown in the diagram. The total elongation (stretch) of the two springs is
  • A
    $\frac{{Mg}}{{{K_1} + {K_2}}}$
  • ✓
    $\frac{{Mg\,({K_1} + {K_2})}}{{{K_1}{K_2}}}$
  • C
    $\frac{{Mg\,{K_1}{K_2}}}{{{K_1} + {K_2}}}$
  • D
    $\frac{{{K_1} + {K_2}}}{{{K_1}{K_2}Mg}}$
✓

Answer

Correct option: B.
$\frac{{Mg\,({K_1} + {K_2})}}{{{K_1}{K_2}}}$
b
(b)For series combination ${k_{eq}} = \frac{{{k_1}{k_2}}}{{{k_1} + {k_2}}}$
$F = {k_{eq}}x \Rightarrow mg = \left( {\frac{{{k_1}{k_2}}}{{{k_1} + {k_2}}}} \right)x$$ \Rightarrow x = \frac{{mg({k_1} + {k_2})}}{{{k_1}{k_2}}}$

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