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4.2 friction — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics4.2 friction1 Mark
MCQ
A man is standing on a rough $(\mu = 0.5)$ horizontal disc rotating with constant angular velocity of $5$ $rad/sec.$ At what distance from centre should he stand so that he does not slip on the disc?
  • ✓
    $R \leq 0.2m$
  • B
    $R > 0.2 m$
  • C
    $R > 0.5 m$
  • D
    $R > 0.3 m$
✓

Answer

Correct option: A.
$R \leq 0.2m$
a
To prevent slipping, centripetal force  $\leq $ frictional force$:$

$F=m R_{\max } \omega^{2}$

$F \leq f \Rightarrow F \leq \mu N[N=m g]$

$\Rightarrow m R_{\max } \omega^{2} \leq \mu m g$

$\Rightarrow R_{\max } \leq \frac{\mu g}{\omega^{2}}=\frac{0.5 \times 5}{5^{2}}$

$\Rightarrow R_{\max } \leq 0.2 m$

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