Question 216: Centre of Mass and Rotational Motion

Question

A ring is hung on a nail. It can oscillate, without
slipping or sliding (i) in its plane with a time
period T1 and, (ii) back and forth in a direction
perpendicular to its plane, with a period T2. The
ratio $${{{T_1}} \over {{T_2}}}$$ will be :

Accepted Answer

Moment of inertia in case (i) is I
1
Moment of inertia in case (ii) is I
2
I
1
= 2MR
2
I
2
= $${1 \over 2}M{R^2}$$ + MR
2
= $${3 \over 2}M{R^2}$$
T
1
= $$2\pi \sqrt {{{{I_1}} \over {Mgd}}} $$
and T
2
= $$2\pi \sqrt {{{{I_2}} \over {Mgd}}} $$
$$ \Rightarrow $$ $${{{T_1}} \over {{T_2}}} = \sqrt {{{{I_1}} \over {{I_2}}}} $$
= $$\sqrt {{{2M{R^2}} \over {{3 \over 2}M{R^2}}}} $$
= $${2 \over {\sqrt 3 }}$$

Answer

$${{\sqrt 2 } \over 3}$$

Answer

$${2 \over {\sqrt 3 }}$$

Answer

$${2 \over 3}$$

Answer

$${3 \over {\sqrt 2 }}$$

Centre of Mass and Rotational Motion

A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T1 and, (ii) back and forth in a direction perpendicular to its plane, with a period T2. The ratio ${{{T_1}} \over {{T_2}}}$ will be :

Choose the correct answer: