Advertisements
Advertisements
Question
Supposing Newton’s law of gravitation for gravitation forces F1 and F2 between two masses m1 and m2 at positions r1 and r2 read F1 = – F2 = `- r_12/r_12^3 GM_0^2 ((m_1m_2)/M_0^2)^n` where M0 is a constant of dimension of mass r12 = r1 – r2 and n is a number. in such a case.
- the acceleration due to gravity on earth will be different for different objects.
- none of the three laws of Kepler will be valid.
- only the third law will become invalid.
- for n negative, an object lighter than water will sink in water.
Advertisements
Solution
a, c and d
Explanation:
Given, `F_1 = - F_2 = (-r_12)/r_12^3 GM_0^2 ((m_1m_2)/m_0^2)^n`
Acceleration due to gravity, `g = (|F|)/"mass"`
= `(GM_0^2 (m_1m_2)^n)/(r_12^2 (M_0)^(2n)) xx 1/(("mass"))`
Since. g depends upon the position vector, hence it will be different for different objects. As g is not constant, hence constant of proportionality will not be constant in Kepler's third law. Hence, Kepler's third law will not be valid.
As the force is of central nature. .....`[∵ "Force" ∝ 1/r^2]`
Hence, the first two of Kepler's laws will be valid.
For negative n, g = `(GM_0^2 (m_1m_2)^-n)/(r_12^2 (M_0)^(-2n)) xx 1/(("mass"))`
= `(GM_0^(2(1 + n)))/r_12^2 ((m_1m_2)^-n)/(("mass"))`
g = `(GM_0^2)/r_12^2 (M_0^2/(m_1m_2)) xx 1/"mass"`
As M0 > m1 or m2
g > 0, hence in this case situation will reverse i.e., an object lighter than water will sink in water.
APPEARS IN
RELATED QUESTIONS
State Kepler's law of orbit and law of equal areas.
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.
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?
Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be \[\sqrt{8}\] T.
Identify the law shown in the figure and state three respective laws.
In the Following figure shows the elliptical path of a planet about the sun. The two shaded parts have equal area. If t1 and t2 be the time taken by the planet to go from a to b and from c to d respectively,
Answer the following question.
State Kepler’s law of equal areas.
The orbit of a planet revolving around a star is _______.
The square of its period of revolution around the sun is directly proportional to the _______ of the mean distance of a planet from the sun.
The earth moves around the sun in an elliptical orbit as shown in the figure. The ratio, `"OA"/"OB"` = x. The ratio of the speed of the earth at Band at A is ______.
To verify Kepler's third law graphically four students plotted graphs. Student A plotted a graph of T (period of revolution of planets) versus r (average distance of planets from the sun) and found the plot is straight line with slope 1.85. Student B plotted a graph of T2 v/s r3 and found the plot is straight line with slope 1.39 and negative Y-intercept. Student C plotted graph of log T v/s log r and found the plot is straight line with slope 1.5. Student D plotted graph of log T v/s log r and found the plot is straight line with slope 0.67 and with negative X-intercept. The correct graph is of student
Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon ______.
In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They ______.
If the sun and the planets carried huge amounts of opposite charges ______.
- all three of Kepler’s laws would still be valid.
- only the third law will be valid.
- the second law will not change.
- the first law will still be valid.
The centre of mass of an extended body on the surface of the earth and its centre of gravity ______.
- are always at the same point for any size of the body.
- are always at the same point only for spherical bodies.
- can never be at the same point.
- is close to each other for objects, say of sizes less than 100 m.
- both can change if the object is taken deep inside the earth.
Give one example each of central force and non-central force.
What is the direction of areal velocity of the earth around the sun?
Halley's Comet revolves around the sun for a time period of 76 years. The aphelion distance if perihelion is given by 8.9 × 1010 m, will be ______.
(Take, the mass of sun = 2 × 1030 kg and G = 6.67 × 10-11 Nm3/kg2)
What is at one focus of the elliptical orbit of a planet?
