Question 439: Centre of Mass and Rotational Motion

Question

Four identical discs each of mass '$$\mathrm{M}$$' and diameter '$$\mathrm{a}$$' are arranged in a small plane as shown in figure. If the moment of inertia of the system about $$\mathrm{OO}^{\prime}$$ is $$\frac{x}{4} \,\mathrm{Ma}^{2}$$. Then, the value of $$x$$ will be ____________.

Accepted Answer

$$I = 2 	imes \left( {{{M{{\left( {{a \over 2}} ight)}^2}} \over 4}} ight) + 2 	imes \left( {{{M{{\left( {{a \over 2}} ight)}^2}} \over 4} + M{{\left( {{a \over 2}} ight)}^2}} ight)$$
$$ = {{M{a^2}} \over 8} + {{5M{a^2}} \over 8}$$
$$ = {{6M{a^2}} \over 8} = {3 \over 4}M{a^2}$$

Centre of Mass and Rotational Motion

Four identical discs each of mass '$\mathrm{M}' and diameter '\mathrm{a}' are arranged in a small plane as shown in figure. If the moment of inertia of the system about \mathrm{OO}^{\prime} is \frac{x}{4} \,\mathrm{Ma}^{2}. Then, the value of x$ will be ____________.

Choose the correct answer: