Question 226: 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 :

Accepted Answer

to pull up, $$	au $$
F
$$ \ge $$ $$	au $$
mg
$$ \Rightarrow $$ F $$ 	imes $$ R $$ \ge $$ Mg $$ 	imes $$ x
$$ \Rightarrow $$ F
min
= $${{Mg} \over R} 	imes \sqrt {{R^2} - {{\left( {R - a} ight)}^2}} $$
= $$Mg\sqrt {1 - {{\left( {{{R - a} \over R}} ight)}^2}} $$

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: