MCQ
Two solid spheres of different mass, radii and density roll down a rough inclined plane under identical situation. Their time to come down is independent of their ............
- AMass
- BRadius
- CDensity
- ✓All of these
✓
Answer
Correct option: D.
All of these
d
(d)
(d)
For rolling down an inclined plane,
$a_{c m}=\frac{g \sin \theta}{1+\frac{1}{m R^2}}$
For 5 phere of mass $m$ and radius $R, 1=\frac{2}{5} m R^2$
So, $\quad a_{c u}=\frac{g \sin 0}{1-\frac{2}{5}\left({m R^2}^2\right)}=\frac{5}{7} g \sin 0$
As acceleration of centre of mass of rolling body only depends upon angle of inclination,
So, time taken to come down, $t =\sqrt{\frac{2 L}{a_{c h}}}$
$\left(\because L=\frac{1}{2} a_{c n} t^2\right)$
$t=\sqrt{\frac{2 L \times 7}{5 g \sin \theta}}=\sqrt{\frac{14 L}{5 g \sin \theta}}$, where $L=$ length of inclined plane.
Here, $t$ is independent of mass, radius and density of spheres. Option (d) is correct.
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