Define acceleration due to gravity. give expression for effect of height on acceleration due to gravity .
Answers
Define acceleration due to gravity. give expression for effect of height on acceleration due to gravity .
Its value near the surface of the earth is 9.8 ms-2. Therefore, the acceleration due to gravity (g) is given by = GM/r2.
Formula: g = GM/r2
Formula: g = GM/r2Values of g in SI: 9.806 ms-2
Formula: g = GM/r2Values of g in SI: 9.806 ms-2SI Unit: ms-2
Answer:
Acceleration due to gravity is the acceleration gained by a body or object due to gravitational force.
Explanation:
Expression for effect of height on acceration due to gravity :-
Consider a test mass (m) at a height (h) from the surface of the earth. Now, the force acting on the test mass due to gravity is;
F = GMm/(R+h)2
Where M is the mass of earth and R is the radius of the earth. The acceleration due to gravity at a certain height is ‘h’ then,
mgh= GMm/(R+h)2
⇒ gh= GM/[R2(1+ h/R)2 ] . . . . . . (2)
The acceleration due to gravity on the surface of the earth is given by;
g = GM/R2 . . . . . . . . . (3)
On dividing equation (3) and (2) we get,
gh = g (1+h/R)-2. . . . . . (4)
This is the acceleration due to gravity at a height above the surface of the earth. Observing the above formula carefully we can say that the value of g decreases with increase in height of an object and the value of g becomes zero at infinite distance from the earth.