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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
$A$ body kept on a smooth horizontal surface is pulled by a constant horizontal force applied at the top point of the body. If the body rolls purely on the surface, its shape can be : 
  • ✓
    thin pipe
  • B
    uniform cylinder
  • C
    uniform sphere
  • D
    thin spherical shell
✓

Answer

Correct option: A.
thin pipe
a
For translation motion of $C . M$

$a=\frac{F+f}{m}$

for roational motional about $C . M$ of

$R(F-f)=I \alpha$

$\alpha=\frac{R}{I}(F-f)$

For pure rolling $a=R \alpha$

$\frac{F+f}{m}=\frac{R^{2}}{I}(F-f)$

$f\left(1+\frac{m R^{2}}{I}\right)=F\left(\frac{m R^{2}}{I}-1\right)$

$f=\frac{\left(m R^{2}-I\right)}{m R^{2}+I} F$

For ring//thin pipe $I=m R^{2},$ so $f=0$ therefore for rolling of ring//thin pipe does not need friction.   

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