Question

write an expression for acceleration due to gravity and determine its value​

Answer 1

Answer:

Explanation:

Acceleration due to Gravity – Formula, Unit and Values

Acceleration Due to Gravity - (g)

Symbol - g

Dimensional Formula- M0L1T-2

SI Unit -ms-2

Formula- g = GM/r2

Values of g in SI -9.806 ms-2

Values of g in CGS -980 cm s-2

Answer 2

Answer:

Expression for acceleration due to gravity 'g'

Consideration:-

Let mass of the object = m

And acceleration due to gravity = g

Proof:-

➥According to Newton's second law of motion:

Force = mass × accelerationForce=mass×acceleration

Therefore,

➪F = m × g....................(I)F=m×g....................(I)

➥Now, according to Universal Law of gravitation,

➪F= G.M.m/d^2 ...................(ii)F=G.M.m/d

2

...................(ii)

➥Thus, put the value of 'F' from (I) in (ii)

⟹ mg= G.M.m/d^2⟹mg=G.M.m/d

2

⟹ g= GM/d^2 ..................(iii)⟹g=GM/d

2

..................(iii)

➥Where , g is acceleration due to gravity,

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'G' is the Universal Gravitational Constant.

'M' is the mass of earth

And 'd' is the distance between object and center of earth.

But when object is near the surface of earth.

When an object is near the surface of earth, the distance between object and center of the earth will be equal to the radius of earth because the distance of centre is negligible in comparison of the radius of earth.

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Let the radius of earth is equal to 'R'

Therefore,

after substitution 'R' at the place of 'd' we get,

⟹ g = GM/R^2⟹g=GM/R

2

➥This is expression of acceleration due to gravity