A uniform disc and a hollow right circular cone have the same for… - Vidyadip

Question

A uniform disc and a hollow right circular cone have the same formula for their M.I., when rotating about their central axes. Why is it so?

✓

Answer

The radius of gyration of a thin ring of radius $Rr$ about its transverse symmetry axis is
$
K _{ r }=\sqrt{I_{ CM } / M_{ r }}=\sqrt{R_{ r }^2}= R _{ r }
$
The radius of gyration of a thin disc of radius $R_d$ about its transverse symmetry axis is
$
k_{ d }=\sqrt{I_{ CM } / M_{ d }}=\sqrt{\frac{M_{ d } R_{ d }^2 / 2}{M_{ d }}}=\frac{1}{\sqrt{2}} R_{ d }
$
Given $k_{ r }=k_{ d }$,
$R_{ r }=\frac{1}{\sqrt{2}} R_{ d }$ or, equivalently, $R_{ d }=\sqrt{2} R_{ r }$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following in Brief" from Rotational Dynamics→Rotational Dynamics — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

At what temperature will helium molecules have the same rms speed as that of hydrogen molecules at STP ? (Molar mass of hydrogen $=2 \mathrm{~g} / \mathrm{mol}$, molar mass of helium $=4 \mathrm{~g} / \mathrm{mol}$ )

How much amount of work is done in forming a soap bubble of radius r?

Express the kinetic energy of a rotating body in terms of its angular momentum.

A solenoid $40 \ cm$ long has a cross-sectional area of $0.9 \ cm^ 2$ and is tightly wound with wire of diameter $1 \ mm$. Calculate the self inductance of the solenoid.

What is heat? Explain.

A parallel plate capacitor filled with air has an area of \(6 cm ^2\) and plate separation of \(3 mm\). Calculate its capacitance.

What will be the effect on the position of zero deflection if only the current flowing through the potentiometer wire is
(i) increased (ii) decreased.

Explain the reflection of transverse and longitudinal waves from a denser medium and a rarer medium.

An electron in a $TV$ picture tube moves horizontally with a speed $2 \times 10^7 m / s$. It is deflected upward by a horizontal magnetic field of induction $10^{-3} T$. Find the magnitude of the force acting on the electron due to the action of the magnetic field.

Prove that a pipe of length $2 L$ open at both ends has the same fundamental frequency as a pipe of length $L$ closed at one end.