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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
The following bodies,

$(1)$ a ring

$(2)$ a disc

$(3)$ a solid cylinder

$(4)$ a solid sphere,

of same mass $m$ and radius $R$ are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ...........

[Mark the body as per their respective numbering given in the question]

  • A
    $2$
  • B
    $3$
  • ✓
    $4$
  • D
    $1$
✓

Answer

Correct option: C.
$4$
c
$Mg \sin \theta R =\left( mk ^{2}+ mR ^{2}\right) \alpha$

$\alpha=\frac{ Rg \sin \theta}{ k ^{2}+ R ^{2}} \Rightarrow a =\frac{ g \sin \theta}{1+\frac{ k ^{2}}{ R ^{2}}}$

$t =\sqrt{\frac{2 s }{ a }}=\sqrt{\frac{2 s }{ g \sin \theta}\left(1+\frac{ k ^{2}}{ R ^{2}}\right)}$

for least time, $k$ should be least $\&$ we know $k$ is least for solid sphere.

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