Question 449: Centre of Mass and Rotational Motion

Question

Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius '2R' are as follows:
I
1
= M.I. of solid sphere about its diameter
I
2
= M.I. of solid cylinder about its axis
I
3
= M.I. of solid circular disc about its diameter
I
4
= M.I. of thin circular ring about its diameter
If 2(I
2
+ I
3
) + I
4
= x . I
1
, then the value of x will be __________.

Accepted Answer

$$2\left( {{1 \over 2} + {1 \over 4}} ight) 	imes M{(2R)^2} + {1 \over 2}M{(2R)^2} = x{2 \over 5}M{(2R)^2}$$
$$ \Rightarrow 1 + {1 \over 2} + {1 \over 2} = x 	imes {2 \over 5}$$
$$ \Rightarrow x = 5$$

Centre of Mass and Rotational Motion

Integer / Numeric Answer Type