Kepler's Law

Q.

A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is

1. 4.8 hours

2. $48\sqrt{2}$ hours

3. 24 hours

4. $24\sqrt{2}$ hours

Q. A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed, (b) angular speed, (c) angular momentum, (d) kinetic energy, (e) potential energy, (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

Q. Two satellite s1 and s2 revolve round a planet in coplanar circular orbits in the same sense. Their period of revolution are 1 hour and 8 hours respectively. The radii of orbit of s1 is 10^ 4 km. When s2 is closest to s1, the angular speed of s2 as actually observed by an astronaut in s1

Q. The eccentricity of earths orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is.

Q. How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 10⁸ km.

Q. If a planet is suddenly stopped in its orbit, suppossed to be circular then it would fall in the sun in a time___?

Q. 11. Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite therefore, they can collide. Total mechanical energy of the system ( both satallites and earths) is (m<

Q.

Kepler's second law regarding constancy of aerial velocity of a planet is a consequence of the law of conservation of

1. Energy

2. Linear momentum

3. None of these

4. Angular momentum

Q.

When a satellite in a circular orbit around the earth enters the atmospheric region, it encounters small air resistance to its motion. Then -

1. Its kinetic energy remains constant

2. Its kinetic energy decreases

3. Its angular momentum about the earth decreases

4. Its period of revolution around the earth increases

Q.

A satellite of mass m moves along an elliptical path around the earth. The areal velocity of the satellite is proportional to

1. m^-1

2. m⁰

3. m^1/2

4. m

Q. An object of mass m is projected upwards with velocity vo/2 from the surface of the Earth. The maximum height reached by the object from the surface of the Earth will be (v0 is orbital velocity near Earth surface, R is radius of the Earth)

Q.

If a body describes a circular motion under inverse square field, the time taken to complete one revolution, T is related to the radius of the circular orbit as

1. 

2. 

3. 

4. 

Q.

Which law governs the phenomenon that a tablecloth is pulled out from under a setting of chinaware without damaging it?

1. Newton’s second law

2. Newton’s first law

3. Universal law of gravitation

4. Newton’s third law

Q. Two particles A and B of mass 1 kg and 4 kg respectively approach each other due to their mutual gravitational force only.Then the ratio of acceleration of A to B at any ins†an t i

Q. Consider a ring of mass m and radius r. Maximum gravitational intensity on the axis of the ring has the valu

Q. Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth ?

Q. 79.Two satellite each of mass m are revolving around earth of mass m. The ratio of maximum amd minimum force on earth due to two satellite is

Q. a disc of radius 2 m and mass 100 kg rolls on a horizontal floor.its centre of mass has speed of 20m/s.how much work is needed to stop it

Q. The time period of polar satellites is about (take $g=9.8{\text{ms}}^{-2}$ and radius of the Earth
$R=6.3\times {10}^6\text{m}$),

[Height of a polar satellite above earth's surface will be around $700\text{km}$]

1. $100\text{min}$
2. $6\text{hr}$
3. $24\text{hr}$
4. $1000\text{min}$

Q. Why acceleration due to gravity is zero when a satellite revolves around the earth? Why it experiences zero gravity or weightlessness?

Q.

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth :

1. The acceleration of S always directed towards the centre of the earth

2. The angular momentum of S about the cente of the earth changes in direction, but its magnitude remain constant

3. The total mechanical energy of S varies periodically with time

4. The linear momentum of S remains constant in magnitude

Q.

A stone of mass m tied to a string of length l is rotating along a circular path with constant speed v. The torque on the stone is

1. Zero

2. mv/l

3. mvl

4. mv²/l

Q. A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is 1.50× 10⁸ km away from the sun ?

Q. Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22 × 10⁸ m. Show that the mass of Jupiter is about one-thousandth that of the sun.

Q. Let us assume that our galaxy consists of 2.5 × 10¹¹ stars each of one solar mass. How long will a star at a distance of 50, 000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be 10⁵ ly.

Q.

A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is

1. 4.8 hours

2. 

3. 24 hours

4. 

Q. How does gravity affect the surrounding

Q. Tow cars having masses m₁ and m₂ moves in circles of radii r₁ and r₂ respectively. If they complete the circle in equal time, the ratio of their angular speed ω₁/ω₂ is
(a) m₁/m₂
(b) r₁/r₂
(c) m₁r₁/m₂/r₂
(d) 1.

Q.

A double star consists of two stars having masses m and 2m separated by a distance r. Which of the following statement is correct?

1. Radius of circular path of star of mass 2m is $\frac{2r}{3}$

2. Kinetic energy of 2 m mass star is double that of lighter star

3. Time period of revolutionof both are not same

4. Angular momentum of lighter star about their centre of mass is more

Q. define 2nd law of kepler regarding planetary motion.