t=cx^2+dx find acceleration in terms of gravity
Answers
Explanation:
Gravity is the force with which earth attracts a body towards its centre. Let us consider two bodies of masses ma and mb. Under the application of equal forces on two bodies, the mass in terms of mass is given by:
mb = ma [aA/aB] this is called an inertial mass of a body.
Under the gravitational influence on two bodies, the mass in terms of mass is given by,
FA = GMmA/r2,
FB = GMmB/r2,
mB = [FB/FA] × mA
⇒ More on Gravitation:
Newton’s Law of Gravitation
Gravitational Potential Energy
Gravitational Field Intensity
The above mass is called a gravitational mass of a body. According to the principle of equivalence, the inertial mass and gravitational mass are identical. We will be using this while deriving acceleration due to gravity given below.
Let us suppose a body [test mass (m)] is dropped from a height ‘h’ above the surface of the earth [source mass (M)], it begins to move downwards with an increase in velocity as it reaches close to the earth surface.
We know that velocity of an object changes only under the action of a force, in this case, the force is provided by the gravity.
Under the action of gravitational force, the body begins to accelerate toward the earth’s centre which is at a distance ‘r’ from the test mass.
Then, ma = GMm/r2 (Applying principle of equivalence)
⇒ a = GM/r2 . . . . . . . (1)
The above acceleration is due to the gravitational pull of earth so we call it as acceleration due to gravity, it does not depend upon the test mass. Its value near the surface of the earth is 9.8 ms-2.
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