1. Tardigrade
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  4. 5-11 Two identical semicircular discs of mass ' m ' each and radius ' R ' are placed in the X Y (horizontal) plane and the Y Z (vertical) plane, respectively. They are so placed that they have their common diameter along the Y-axis. Then, the moment of inertia (In) of the system about the appropriate axis is given by (In. refers to moment of inertia about axis n-where n is X, Y, Z )

Q. 5-11 Two identical semicircular discs of mass ' $m$ ' each and radius ' $R$ ' are placed in the $X Y$ (horizontal) plane and the $Y Z$ (vertical) plane, respectively. They are so placed that they have their common diameter along the $Y$-axis. Then, the moment of inertia $\left(I_{n}\right)$ of the system about the appropriate axis is given by $\left(I_{n}\right.$ refers to moment of inertia about axis $n$-where $n$ is $X, Y, Z$ )

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Solution:

image
From figure we have
$I_{Y}=\frac{1}{2} m R^{2} \quad \& I_{X}=I_{Z}=\frac{3}{4} m R^{2}$

Questions from System of Particles and Rotational Motion

1. A disc is rolling, the velocity of its centre of mass is $V_{cm}$. Which one of these will be correct ?

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2. The centre of mass of a system of three particles of masses $1\,g, 2\,g$ and $3\,g$ is taken as the origin of a coordinate system. The position vector of a fourth particle of mass $4\, g$ such that the centre of mass of the four particle system lies at the point $(1, 2, 3)$ is a $(\hat i + 2 \hat j + 3 \hat k)$ , where a is a constant. The value of $\alpha$ is

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