Question 225: Centre of Mass and Rotational Motion

Question

A uniform cylinder of mass M and radius R is to
be pulled over a step of height a (a < R) by
applying a force F at its centre ‘O’
perpendicular to the plane through the axes of
the cylinder on the edge of the step (see
figure). The minimum value of F required is :
![](https://imagex.cdn.examgoal.net/jgy2xukev0w7l6/77ffb717-b5e3-4c27-93f5-8f69db370fb6/a7820ca0-f268-11ea-8293-3b6cc591631c/file-jgy2xukev0w7l7-311w.png)

Accepted Answer

to pull up, $	au $
F
$ \ge $ $	au $
mg
$ \Rightarrow $ F $ 	imes $ R $ \ge $ Mg $ 	imes $ x
$ \Rightarrow $ F
min
= ${{Mg} \over R} 	imes \sqrt {{R^2} - {{\left( {R - a} ight)}^2}} $
= $Mg\sqrt {1 - {{\left( {{{R - a} \over R}} ight)}^2}} $
![](https://imagex.cdn.examgoal.net/1ki2194cm/a2ea5501-a071-464c-a6cf-d9e93e5ffc5b/31358570-31a8-11eb-85f3-377f9df5d1a5/file-1ki2194cn-421w.png)

Answer

$Mg\sqrt {1 - {{\left( {{{R - a} \over R}} \right)}^2}} $

Answer

$Mg\sqrt {1 - {{{a^2}} \over {{R^2}}}} $

Answer

$Mg{a \over R}$

Answer

$Mg\sqrt {{{\left( {{R \over {R - a}}} \right)}^2} - 1} $

Centre of Mass and Rotational Motion

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is :

Choose the correct answer: