A binary star consists of two stars $\mathrm{A}$ (mass $2.2 \mathrm{M}_5$ ) and $\mathrm{B}$ (mass $11 \mathrm{M}_5$ ), where $\mathrm{M}_5$ is the mass of the sun. They are separated by distance $\mathrm{d}$ and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star $\mathrm{A}$ to the angular momentum of star $\mathrm{B}$ about the centre of mass is
A binary star consists of two stars $\mathrm{A}$ (mass $2.2 \mathrm{M}_5$ ) and $\mathrm{B}$ (mass $11 \mathrm{M}_5$ ), where $\mathrm{M}_5$ is the mass of the sun. They are separated by distance $\mathrm{d}$ and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star $\mathrm{A}$ to the angular momentum of star $\mathrm{B}$ about the centre of mass is
- [IIT 2010]
- A
$1$
- B
$2$
- C
$4$
- D
$6$
Similar Questions
Angular momentum of a single particle moving with constant speed along circular path:
Angular momentum of a single particle moving with constant speed along circular path:
- [JEE MAIN 2021]
A particle of mass $m$ is moving along the side of a square of side '$a$', with a uniform speed $v$ in the $x-y$ plane as shown in the figure
Which of the following statement is false for the angular momentum $\vec L$ about the origin ?
A particle of mass $m$ is moving along the side of a square of side '$a$', with a uniform speed $v$ in the $x-y$ plane as shown in the figure
Which of the following statement is false for the angular momentum $\vec L$ about the origin ?
- [JEE MAIN 2016]
In the List-$I$ below, four different paths of a particle are given as functions of time. In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha \neq \beta$. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: $\overrightarrow{ p }$ is the linear momentum, $\bar{L}$ is the angular momentum about the origin, $K$ is the kinetic energy, $U$ is the potential energy and $E$ is the total energy. Match each path in List-$I$ with those quantities in List-$II$, which are conserved for that path.
List-$I$
List-$II$
$P$ $\dot{r}(t)=\alpha t \hat{t}+\beta t \hat{j}$
$1$ $\overrightarrow{ p }$
$Q$ $\dot{r}(t)=\alpha \cos \omega t \hat{i}+\beta \sin \omega t \hat{j}$
$2$ $\overrightarrow{ L }$
$R$ $\dot{r}(t)=\alpha(\cos \omega t \hat{i}+\sin \omega t \hat{j})$
$3$ $K$
$S$ $\dot{r}(t)=\alpha t \hat{i}+\frac{\beta}{2} t^2 \hat{j}$
$4$ $U$
$5$ $E$
In the List-$I$ below, four different paths of a particle are given as functions of time. In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha \neq \beta$. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: $\overrightarrow{ p }$ is the linear momentum, $\bar{L}$ is the angular momentum about the origin, $K$ is the kinetic energy, $U$ is the potential energy and $E$ is the total energy. Match each path in List-$I$ with those quantities in List-$II$, which are conserved for that path.
| List-$I$ | List-$II$ |
| $P$ $\dot{r}(t)=\alpha t \hat{t}+\beta t \hat{j}$ | $1$ $\overrightarrow{ p }$ |
| $Q$ $\dot{r}(t)=\alpha \cos \omega t \hat{i}+\beta \sin \omega t \hat{j}$ | $2$ $\overrightarrow{ L }$ |
| $R$ $\dot{r}(t)=\alpha(\cos \omega t \hat{i}+\sin \omega t \hat{j})$ | $3$ $K$ |
| $S$ $\dot{r}(t)=\alpha t \hat{i}+\frac{\beta}{2} t^2 \hat{j}$ | $4$ $U$ |
| $5$ $E$ |
- [IIT 2018]
A metre stick is pivoted about its centre. A piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m / s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg m ^2$, the initial angular velocity of the stick is ........... $rad / s$
A metre stick is pivoted about its centre. A piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m / s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg m ^2$, the initial angular velocity of the stick is ........... $rad / s$
A small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion is the $x-y$ plane with centre at $O$ and constant angular speed $\omega$. If the angular momentum of the system, calculated about $O$ and $P$ are denoted by $\vec{L}_O$ and $\vec{L}_P$ respectively, then
A small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion is the $x-y$ plane with centre at $O$ and constant angular speed $\omega$. If the angular momentum of the system, calculated about $O$ and $P$ are denoted by $\vec{L}_O$ and $\vec{L}_P$ respectively, then
- [IIT 2012]