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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
An inclined plane makes an angle of ${30^o}$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to 
  • A
    $\frac{g}{3}$
  • B
     $\frac{{2g}}{3}$
  • C
    $\frac{{5g}}{7}$
  • ✓
    $\frac{{5g}}{{14}}$
✓

Answer

Correct option: D.
$\frac{{5g}}{{14}}$
d
$a=\frac{m g \sin \theta-F}{m}$

$\alpha=\frac{F R}{I}=\frac{5 F R}{2 M R^{2}}=\frac{5 F}{2 M R}$

For no slipping, $R \alpha=a$

$\frac{5 F}{2 M}=g \sin \theta-\frac{F}{M} \Rightarrow \frac{F}{M}=\frac{2}{7} g \sin \theta$

$a=g \sin \theta \cdot \frac{F}{M}=\frac{5}{7} g \sin \theta=\frac{5}{7} g \sin 30$

$=\frac{5}{14} g$

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