A comet revolves around the sun in a highly elliptical orbit having a minimum distance of $7 \times 10^{10}m$ and a maximum distance of $1.4 \times 10^{13}m$. If its speed while nearest to the Sun is $60km s^{-1}$, find its linear speed when situated farthest from the Sun.
Download our app for free and get started
Let mass of comet be M and its angular speed be w when situated at a distance r from the Sun, then its angular momentum $L = I w = Mr^2w$ If v be the linear speed, then $L = Mr^2w = Mrv$ In accordance with conservation law of angular momentum, we can write that $\text{Mr}_1\text{v}_1=\text{mr}_2\text{v}_2$
$\therefore\text{v}_2=\frac{\text{r}_1\text{v}_1}{\text{r}_2}=\frac{7\times10^{10}\text{m}\times60\text{km/s}}{1.4\times10^{13}\text{m}}$ $=0.3\text{km/s}\text{ or }300\text{m/s.}$
$\therefore\text{v}_2=\frac{\text{r}_1\text{v}_1}{\text{r}_2}=\frac{7\times10^{10}\text{m}\times60\text{km/s}}{1.4\times10^{13}\text{m}}$ $=0.3\text{km/s}\text{ or }300\text{m/s.}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionSuppose the particle of the previous problem has a mass m and a speed v before the collision and it sticks to the rod after the collision. The rod has a mass M:
- Find the velocity of the centre of mass C of the system constituting ''The rod plus the particle''.
- Find the velocity of the particle with respect to C before the collision.
- Find the velocity of the rod with respect to C before the collision.
- Find the angular momentum of the particle and of the rod about the centre of mass C before the collision.
- Find the moment of inertia of the system about the vertical axis through the centre of mass C after the collision.
- Find the velocity of the centre of mass C and the angular velocity of the system about the centre of mass after the collision.
- 2A solid sphere of mass 0.50kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is $\frac{2}{7}.$ What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?View Solution
- 3View SolutionHow much fraction of the kinetic energy of rolling is purely:
- Translational.
- Rotational.
- 4The distance between the centres of carbon and oxygen atoms in carbon monoxide gas molecules is $=1.13\mathring{\text{A}}.$ Locate the centre of mass of the molecules relative to carbon atom.View Solution
- 5A solid disc and a ring, both of radius $10cm$ are placed on a horizontal table simultaneously, with initial angular speed equal to $10 π$ rad $s^{-1}$. Which of the two will start to roll earlier? The co-efficient of kinetic friction is $\mu_\text{k}=0.2$View Solution
- 6Two particles of mass $2kg$ and $1kg$ are moving along the same line with speeds $2ms-1$ and $5ms^{-1}$ respectively. What is the speed of the centre of mass of the system if both the particles are moving (a) in same direction (b) in opposite direction?View Solution
- 7View SolutionA threaded rod with 12turns/ cm and diameter 1.18cm is mounted horizontally. A bar with a threaded hole to match the rod is screwed onto the rod. The bar spins at 216rev/ min. How long will it take for the bar to move 1.50cm along the rod?
- 8A meter stick held vertically, with one end on the ground, is then allowed to fall. What is the value of the radial and tangential acceleration of the top end of the stick when the stick has turned through on angle $\theta?$ What is the speed with which the top end of the stick hits the ground? Assume that the end of the stick in. contact with the ground does not slip.View Solution
- 9Particles of masses $1g, 2g, 3g, ........, 100g$ are kept at the marks $1cm, 2cm, 3cm, ........, 100cm$ respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.View Solution
- 10The descending pulley shown in figure has a radius $20cm$ and moment of inertia $0.20kg-m^2$. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is $1.0kg$.View Solution
