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Maharashtra Class 9 Answered

    give scientific reason  when an object falls freely to the ground its acceleration is uniform  
Asked by rajendrapagar58 | 30 Jun, 2019, 02:05: PM
answered-by-expert Expert Answer
If the object is at a height h above earth's surface, attractive force F acting on an object of mass m due to gravitation
is given by, begin mathsize 14px style F space equals space G fraction numerator M space m over denominator open parentheses R plus h close parentheses squared end fraction end style ....................(1)
Where G is gravitational constant, M is mass of earth, R is radius of earth.
 
Since earth's radius is 6378 km, for few meter or around 1 km distance,
we can approximate (R+h) ≈ R and rewrite eqn.(1) as begin mathsize 14px style F space equals space G fraction numerator M space m over denominator R squared end fraction end style ................(2)
Since acceleration of the object is F/m,  acceleration g for freely falling body is given by,   g =  GM/R2 ...............(3)
 
We see from eqn.(3), Right side of eqn.(3) has only constants . Hence acceleration for a freely falling body is uniform
Answered by Thiyagarajan K | 30 Jun, 2019, 03:02: PM
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