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6. system of particles and rotational motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
A solid sphere rolls without slipping and presses a spring of spring constant $'k'$ as shown  in figure. Then, the compression in the spring will be :-
  • A
    $v\sqrt {\frac{{2m}}{{3k}}} $
  • B
    $v\sqrt {\frac{{5k}}{{7m}}} $
  • C
    $v\sqrt {\frac{{2m}}{{5k}}} $
  • ✓
    $v\sqrt {\frac{{7m}}{{5k}}} $
✓

Answer

Correct option: D.
$v\sqrt {\frac{{7m}}{{5k}}} $
d
By conservation of energy

$\frac{1}{2} \mathrm{mv}^{2}\left(1+\frac{2}{5}\right)=\frac{1}{2} \mathrm{kx}^{2}$

$\Rightarrow \operatorname{mv}^{2}\left(\frac{7}{5}\right)=\mathrm{kx}^{2}$

$\Rightarrow x=v \sqrt{\frac{7 m}{5 k}}$

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