A uniform horizontal disc is freely rotating about a vertical axi… - Vidyadip

Question

A uniform horizontal disc is freely rotating about a vertical axis passing through its centre at the rate of $180 \mathrm{rpm}$. A blob of wax of mass $1.9 \mathrm{~g}$ falls on it and sticks to it at $25 \mathrm{~cm}$ from the axis. If the frequency of rotation is reduced by $60 \mathrm{rpm}$, calculate the moment of inertia of the disc.

✓

Answer

Data : $\mathrm{f}_1=180 \mathrm{rpm}=180 / 60 \mathrm{rot} / \mathrm{s}=3 \mathrm{rot} / \mathrm{s}, \mathrm{f}_2=(180-60) \mathrm{rpm}=120 / 60 \mathrm{rot} / \mathrm{s}=2 \mathrm{rot} / \mathrm{s}, \mathrm{m}$ $=1.9 \mathrm{~g}=1.9 \times 10^{-3} \mathrm{~kg}, \mathrm{r}=25 \mathrm{~cm}=0.25 \mathrm{~m}$
Let $I_1$ be the $M l$ of the disc. Let $I_2$ be the Ml of the disc and the blob.
$
\therefore I_2=I_1+m r^2
$
According to the principle of conservation of angular momentum,
$
\begin{aligned}
& I_1 \omega_1=I_2 \omega_2 \quad \\
& \therefore I_1\left(2 \pi f_1\right)=\left(I_1+m r^2\right)\left(2 \pi f_2\right) \\
& \therefore I_1 f_1=\left(I_1+m r^2\right) f_2 \\
& \therefore I_1\left(f_1-f_2\right)=m r^2 f_2 \\
& \therefore I_1=\frac{m r^2 f_2}{f_1-f_2}=\frac{1.9 \times 10^{-3} \times(0.25)^2 \times 2}{3-2} \\
& =3.8 \times 10^{-3} \times 6.25 \times 10^{-2} \\
& =2.375 \times 10^{-4} \mathrm{~kg} \cdot \mathrm{m}^2 \\
&
\end{aligned}
$

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 "Short Answer Type Question" 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

$3$ mole of a gas at temperature $400\ K$ expands isothermally from an initial volume of $4$ litres to a final volume of $8$ litres. Find the work done by the gas. $(R = 8.31 J mol^{-1} K^{-1})$

A search coil having $2000$ turns with area $1.5 cm^2$ is placed in a magnetic field of $0.60$ T . The coil is moved rapidly out of the field in a time of $0.2$ second. Calculate the induced emf across the search coil.

What causes viscous drag in fluids?

What is the internal resistance of the cell ?

The spin dryer of a washing machine rotating at $15 r.p.s$. slows down to $5 r.p.s$. after making $50$ revolutions.
Find its angular acceleration.

White light consists of wavelengths from 400 nm to 700 nm. What will be the wavelength range seen when white light is passed through a glass of refractive index 1.55?

Two wheels have the same mass. First wheel is in the form of a solid disc of radius $\mathrm{R}$ while the second is a disc with inner radius $r$ and outer radius $R$. Both are rotating with same angular velocity $\omega_0$ about transverse axes through their centres. If the first wheel comes to rest in time $t_1$ while the second comes to rest in time $t_2$, are $t_1$ and $t_2$ different? Why?

State the relation between the SI units volt and weber.

In circular motion, assuming \(\vec{v}=\vec{\omega} \times \vec{r}, 01\), olbtain an expression for the resultant acceleration of a particle in terms of tangential and radial component.

In a refrigerator, in one cycle, the external work done on the working substance is $20 \%$ of the energy extracted from the cold reservoir. Find the coefficient of performance of the refrigerator.