Free Fall Under Gravity
Free Fall Under Gravity
Free Fall Under Gravity: Whenever objects fall towards the earth under the earth’s gravitational force alone, then these are called freely falling objects and such a motion is called free fall.
Acceleration due to Gravity (g): Whenever an object falls towards the earth, acceleration is involved. This acceleration is due to the earth’s gravitational pull and is called acceleration due to gravity (or acceleration due to the gravitational force of the earth). It is denoted by g. The SI unit of ‘g’ is the same as that of acceleration, i.e. . Let mass of the earth be ‘M’ and an object falling freely towards it be ‘m’. The distance between centres of the earth and the object is ‘R.’ From Newton’s law of gravitation,
Also, from second law of motion, force exerted on object, F = ma. Since, a = g (i.e. acceleration due to gravity); F = mg. Equating RHS of Eqs. (i) and (ii), we get
From the formula, it is clear that acceleration due to gravity does not depend on the mass of a falling object. It depends only on the mass of the earth or celestial bodies. As distance of an object from the centre of the celestial body increases, the value of g decreases. Earth is flattened at poles. Thus, radius of the earth is less at poles than at equator. Hence, the value of g is less at equator than at poles.
Calculation of value of g: To calculate the value of g, we should put the values of G, M and R in the above formula
Mass of Earth
Radius of Earth
Universal gravitational constant,
Motion of Objects under the Influence of Gravitational Force of the Earth: The three equations of motion we have derived earlier is for bodies under uniform acceleration. Since, in case of motion of bodies under free fall, there is also a uniform acceleration, i.e. acceleration due to gravity (g) acting downwards. So the previous three equations of motion can be applied for the motion of bodies under free fall as follows:
Where, ‘h’ is the height from which the object falls, ‘t’ is the time fall, ‘u’ is the initial velocity and ‘v’ is the final velocity when body accelerates at g.
In solving numerical problems, we should remember the following points:
1. If an object falls vertically downwards, then acceleration due to gravity is taken as positive, since its velocity increases while falling.
2. If an object is thrown vertically upwards, then acceleration due to gravity is taken as negative, since its velocity decreases as it moves upward.
Q. A ball is thrown vertically upwards with a velocity of 25 m/s. If g is , then calculate (i) height it reaches (ii) time taken to return back.
Solution: Given, initial velocity, u = 25 m/s, fianl velocity, v = 0
If a body is thrown upwards, then its velocity becomes zero at highest point, where it reaches, acceleration due to gravity,
(i) Heiight,
(ii)
Time taken to return back, T = time of ascent + time of descent = 2t
Time taken to return back, T =
A ball is thrown vertically upwards. It has a speed of | |||
| Right Option : A | |||
| View Explanation | |||
A ball is thrown up with a velocity of 20 ms-1. The time taken by the ball to come back to Earth's surface is (taken g = 10 m/s2) | |||
| Right Option : D | |||
| View Explanation | |||
Which of the following are correct : (a) Acceleration due to the gravitational force of the earth is denoted by g. (b) Acceleration due to gravity does not depend on the mass of a falling object. (c) Acceleration due to gravity does not depend only on the mass of the earth or celestial bodies. | |||
| Right Option : D | |||
| View Explanation | |||
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