MHT CET 2024 10th May Morning Shift | Rotational Motion Question 47 | Physics

A solid metallic sphere of radius ' $R$ ' having moment of inertia '$I$' about diameter is melted and recast into a solid disc of radius ' $r$ ' of a uniform thickness. The moment of inertia of a disc about an axis passing through its edge and perpendicular to its plane is also equal to '$I$'. The ratio $\frac{r}{R}$ is

$\frac{1}{\sqrt{2}}$

$\frac{2}{\sqrt{5}}$

$\frac{2}{\sqrt{10}}$

$\frac{2}{\sqrt{15}}$

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

A particle of mass ' m ' is rotating in a circular path of radius ' $r$ '. Its angular momentum is ' $L$ ' The centripetal force acting on it is ' $F$ '. The relation between ' $F$ ', ' $L$ ', ' $r$ ' and ' $m$ ' is

$\mathrm{F}=\frac{\mathrm{L}}{\mathrm{mr}^2}$

$\mathrm{L}=\mathrm{m}^2 \mathrm{Fr}^2$

$\frac{\mathrm{L}^2}{\mathrm{~m}}=\mathrm{Fr}^3$

$\frac{\mathrm{F}}{\mathrm{L}^3}=\mathrm{mr}^2$

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

Three thin rods, each mass ' 2 M ' and length ' L ' are placed along $\mathrm{x}, \mathrm{y}$ and z axis which are mutually perpendicular. One end of each rod is at origin. Moment of inertia of the system about x - axis is

$\frac{4 \mathrm{ML}^2}{3}$

$\frac{\mathrm{ML}^2}{12}$

$\frac{\mathrm{ML}^2}{6}$

$\frac{2 \mathrm{ML}^2}{3}$

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

-0

A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of [ $\mathrm{g}=$ gravitational acceleration]

$\frac{\omega^2 \mathrm{~L}^2}{12 \mathrm{~g}^2}$

$\frac{\omega^2 L^2 g}{6}$

$\frac{\omega^2 g}{12 \mathrm{~L}^2}$

$\frac{\omega^2 L^2}{24 \mathrm{~g}}$

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