Important Questions of Gravitation Class 11 Physics: Fully Solved

Ans. Air is required for aeroplane to fly hence the aeroplane requires fuel against the frictional force due to air. On the other hand, the satellite orbits at a much more height where almost no air is present and its friction in negligible.

Ans. The escape velocity $v_{e}=\sqrt{2 g R}$ does not depend upon the mass of the projectile. Thus we need the same velocity to project an elephant and an ant into space.

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Ans. since earth rotates from west to east and as such all points on the earth have velocity from west to east. Moreover, this velocity is maximum in the equatorial plane as . This maximum velocity is added to the launching velocity of the rocket and hence launching becomes easier.

Ans. No, rocket can have any velocity at the start. The rocket can continue to increase the velocity due to thrust provided by the escaping gases that will carry it to a desired position.

Ans. (i) According to the law of conservation of angular momentum, the planet moves faster when it is close to the sun and moves slower when it is farther away from the sun. Hence linear speed of the planet does not remain constant. (ii) According to the law of conservation of angular momentum, the angular momentum of planet remains constant. (iii) Since linear speed of the planet around the sun changes, therefore, its kinetic energy also changes continuously. (iv) Potential energy depends upon the distance between sun and planet, hence potential energy changes as the distance between the sun and planet changes continuously. (v) Total energy of planet remains constant.

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Ans. The upward and downward sense is due to gravitational force of attraction between the body and the earth. In spaceship gravitational force is counter balanced by the centripetal force needed by satellite to move around the earth in circular orbit. Hence in absence of force, the astronaut will not be able to distinguish between up and down.

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Ans. Geo-stationary or Geo-synchronous satellite : A satellite which appears stationary to an observer on earth is called geo-stationary satellite. Obviously, the velocity of such satellite relative to earth is zero. Clearly time of revolution of satellite hrs. This satellite is also called geo-synchronous satellite as its angular velocity is synchronised with angular speed of earth about its axis. i.e. this satellite revolves around the earth with same angular speed in same direction as is done by earth around its axis. Essential conditions for geo-stationary satellite: (a) A geo-stationary satellite should be at a height of nearly $36,000 \mathrm{km}$ above the equator of earth. (b) The period of revolution around the earth should be the same as that of earth about its axis i.e. exactly 24 hours. (c) It should revolve in an orbit concentric and co- planer with the equatorial plane, so the plane of orbit of the satellite in normal to the axis of rotation of the earth. (d) Its sense of rotation should be same as that of earth about its own axis i.e. from west to east. Its orbital velocity is nearly 3.1 $k m /$ sec. Uses : Geo-stationary satellites are used for purposes of communications as they act as reflectors of suitable waves carrying the messages. Hence they are also called telecommunication satellites. India's INSAT- $2 \mathrm{B}, 2 \mathrm{C}$ are communication satellites. Polar satellites : Such satellite which revolves in polar orbit around the earth is called polar satellites. A polar orbit is one whose angle of inclination with equatorial plane of earth is $90^{\circ}$ and a satellite in polar orbit passes over the both north and south geographic poles respectively once in orbit.

(i) For ground water survey. (ii) For detection the areas under forest. (iii) For preparing wasteland maps.

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(iv) For assessment of drought. (v) For the assessment of crop diseases. (vi) For detecting the potential fishing zones. (vii) For identifying the sources of pollution. (viii) To locate the position and movement of the troops of enemy and to locate the place and time for any nuclear explosion etc. i.e. for spying purposes.

Ans.  On the basis of his investigations, Kepler formulated the following three laws of planetary motion: (i) First law (law of orbit): Every planet revolves around the sun in an elliptical orbit, keeping sun at one focus of ellipse. (ii) Second law (Law of area): The radius vector drawn from sun to a planet sweeps out equal areas in equal intervals of time. i.e. areal velocity of the planet around the sun is constant. (iii) Third law (Law of period): The square of time period of revolution of a planet around the sun is directly proportional to the cube of semi major axis of its elliptical orbit i.e. $T^{2} \propto R^{3}$ Deduction of second law: Let a particle rotates in $X-Y$ plane about $z$ -axis. At any time $t, \overrightarrow{O P}=\vec{r},$ be the position vector of particle. The area swept by the position vector in small time $d t,$ $|d \vec{A}|=$ area of $\Delta O P Q=\frac{1}{2}|\vec{r} \times d \vec{r}|$ since, a planet revolves around the sun, in an elliptical orbit under the influence of gravitational pull of sun on planets and this pull (or force) acts along the line joining the centres of the sun and theplanet and is directed towards the sun. Hence, the torque acting on planet is zero. i.e. areal velocity of the planet around the sun is constant, which is second law of planetary motion. Deduction of third law : Let a planet of mass $^{\circ} \mathrm{m}^{\prime}$ is orbiting around the sun of mass $M$ in a circular orbit of radius $^{\circ} r^{\prime}$ with constant angular velocity $\omega,$ then, $\frac{G M m}{r^{2}}=m \omega^{2} r=m\left(\frac{2 \pi}{T}\right)^{2} r \Rightarrow T^{2}=\left(\frac{4 \pi^{2}}{G M}\right) r^{3}$ i.e. $T^{2} \propto r^{3} \quad\left(\because \frac{4 \pi^{2}}{G M}=\text { constant }\right)$ Above result holds equally good for elliptical orbit provided we replace $r$ with $^{*} a^{\prime},$ the semi major axis of ellipse.