GRAVITATION EXERCISE QUESTIONS
1.Study the entries in the following table and rewrite them putting the connected items in a single row.
Gravitation Exercise Questions
Gravitation Exercise Questions
2.Answer the following questions.
a. What is the difference between mass and weight of an object. Will the mass and weight of an object on the earth be same as their values on Mars? Why?
Gravitation Exercise Questions
Mass –
- It is the amount of matter present in an object.
- Its value remains same everywhere.
- It can never be zero
Weight –
- It is the force with which the earth attracts an object.
- It keeps changing from place to place.
- It becomes zero at the centre of earth
It is the product of mass and gravitational acceleration,
i.e., W = F = mg
Hence, the mass of an object on earth will be same as its value on Mars.
As the weight depends on the value of acceleration due to gravity (g) which changes from place-to-place, and is different for earth and Mars, the weight of the object on earth will be different than its value on Mars.
b. What are (i) free fall, (ii) acceleration due to gravity (iii) escape velocity (iv) centripetal force?
Gravitation Exercise Questions
Free fall:
The motion of any object under the influence of the force of gravity alone is called as free fall.
Acceleration due to gravity:
The acceleration produced in a body under the influence of the force of gravity alone is called acceleration due to gravity.
Escape velocity:
The minimum initial velocity with which a body should be projected from the surface of a planet or moon, so that it escapes from the gravitational influence of the planet or moon is called as escape velocity.
Centripetal force:
The force acting on any object moving in a circle and directed towards the centre of the circle is called as centripetal force.
c. Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?
Gravitation Exercise Questions
(i) Kepler’s first law: The orbit of a planet is an ellipse with the Sun at one of the foci.
(ii) Kepler’s second law: The line joining the planet and the Sun sweeps equal areas in equal intervals of time.
(iii) Kepler’s third law: The square of its period of revolution around the Sun is directly proportional to the cube of the mean distance of a planet from the Sun.
Inverse square law derivation –
Centripetal force (F) acting on a planet of mass ‘m’ and velocity ‘v’, revolving at a distance of r from the sun is given as,
F= mv2 / r …
When a planet is moving around the sun, Distance travelled by planet in one revolution = Circumference of orbit = 2πr
Time period of revolution = (T)
∴ speed of planet v = distance / time
V = 2πr / T … (ii)
Substituting eq. (ii) in (i)
∴ F = m (2πr / T )2 / r = m4π2r2 / rT2
∴ F = 4mπ2r / T2
Multiplying numerator and denominator with ‘r2’.
∴ F = 4mπ2r / T2 × r2 / r2
∴ F = 4mπ2r3 / r2T2 … (iii)
According to Kepler’s 3rd law
T2 / r3 = k or r3 / T2 = 1/k … (iv)
Substituting (iv) in (iii)
F = 4mπ2r3 / r2T2 × 1/ k = 4mπ2 / r2k …(v)
Rearranging eq. (v)
F = 4mπ2 / k × 1 / r2
Since 4mπ2 / k = constant.
∴ F = constant × 1/ r2
∴ F α 1/r2
Thus, Newton concluded that, centripetal force is responsible for circular motion of the planet and this force is inversely proportional to square of distance between planet and sun.
Gravitation Exercise Questions
d. A stone thrown vertically upwards with initial velocity u reaches a height ‘h’ before coming down. Show that the time taken to go up is same as the time taken to come down.
e. If the value of g suddenly becomes twice its value, it will become two times more difficult to pull a heavy object along the floor. Why?
Gravitation Exercise Questions
The weight of an object is defined as the force with which the earth attracts the object. This force is given as –
W = F = mg
The weight of an object depends on the mass of the object and the value of acceleration due to gravity.
If the value of g doubles, the force with which the earth attracts the object also becomes twice. Thus, the object becomes twice as heavier, making it harder to be pulled along the floor.
Gravitation Exercise Questions
3.Explain why the value of g is zero at the centre of the earth.
The acceleration due to gravity (g) on earth’s surface is given as,
G = GM / R2
The value of g depends on the mass M of the earth and the radius R of the earth.
As we go inside the earth, our distance from the centre of the earth decreases and no longer remains equal to the radius of the earth (R).
Along-with the distance, the part of the earth which contributes towards the gravitational force felt also decreases, decreasing the value of (M).
Due to combined result of change in R and M, value of g becomes zero at the centre of the earth.
Gravitation Exercise Questions
4. 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 8√ T.
According to Kepler’s third law, the square of orbital period of revolution T of a planet around a star is directly proportional to the cube of the mean distance R of the planet from the star.
΅ T 2 α R 3
T 2 = k (R) 3 …. (1)
Where, k is constant of proportionality.
When the planet is at a distance of 2R from the star, then its period of revolution T’ will be,
T’ 2 α (2R) 3
T’ 2 = k (2R) 3 …. (2)
Dividing equations (1) and (2), we get,
T 2 / T’2 = (R) 3 / (2R) 3
T 2 / T’2 = 1/ 8
T’2 = √8 T
Thus, for a planet at a distance of 2R from the star, its period of revolution will be √8 T
Gravitation Exercise Questions
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Gravitation Exercise Questions