A horizontal disc rotating freely about a vertical axis through i… - Vidyadip

MCQ

A horizontal disc rotating freely about a vertical axis through its centre makes $90$ revolutions per minute. A small piece of wax of mass $m$ falls vertically on the disc and sticks to it at a distance $r$ from the axis. If the number of revolutions per minute reduce to $60$ , then the moment of inertia of the disc is .........

A
$m r^2$
B
$\frac{3}{2} m r^2$
✓
$2{m r^2}^2$
D
$3 mr ^2$

✓

Answer

Correct option: C.

$2{m r^2}^2$

c
(c)

$w_1=\frac{2 \pi 90}{60}=3 \pi rps$

$w_2=\frac{2 \pi 60}{60}=2 \pi rps$

Using angular momentum conservation

$I(1.5)=\left(I+m r^2\right)(1)$

$\frac{1}{2}=m r^2$

$I=2 m r^2$

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

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Two forces of $12 \,N$ and $8 \,N$ act upon a body. The resultant force on the body has maximum value of........$N$

A ring is hung on a nail. It can oscillate, without slipping or sliding $(i)$ in its plane with a time period $T_{1}$ and, $(ii)$ back and forth in a direction perpendicular to its plane, with a period $T _{2}$. the ratio $\frac{ T _{1}}{ T _{2}}$ will be

The distance between charges $5 \times {10^{ - 11}}\,C$ and $ - 2.7 \times {10^{ - 11}}\,C$ is $0.2\, m$. The distance at which a third charge should be placed in order that it will not experience any force along the line joining the two charges is......$m$

A stone is thrown at an angle $\theta $ to the horizontal reaches a maximum height $H$. Then the time of flight of stone will be

As in the figure, if a capacitor of capacitance $C$ is charged by connecting it with resistance $R$, then energy given by the battery will be

A toy gun fires a plastic pellet with a mass of $0.5\ g$. The pellet is propelled by a spring with a spring constant of $1.25\ N/cm$, which is compressed $2.0\ cm$ before firing. The plastic pellet travels horizontally $10\ cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\ N$. What is the speed (in $SI\ units$) of the bullet as it emerges from the barrel?

The quantities $\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}$ and $z=\frac{l}{C R}$ are defined where $C-$ capacitance $R-$Resistance, $l-$length, $E-$Electric field, $B-$magnetic field and $\varepsilon_{0}, \mu_{0},$ -free space permittivity and permeability respectively. Then....

The unit of "impulse per unit area" is same as that of

Electric potential at a point $P$ due to a point charge of $5 \times 10^{-9}\; C$ is $50 \;V$. The distance of $P$ from the point charge is ......... $cm$

(Assume, $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^{+9}\; Nm ^2 C ^{-2}$)

A big drop is formed by coalescing $1000$ small droplets of water. The ratio of surface energy of $1000$ droplets to that of energy of big drop is $\frac{10}{x}$. The value of $x$ is_______.