CBSE Class 11-science Answered
How fast will an object be moving when at infinity if it is launched with a speed of 22.4km/s from the surface of earth
Asked by Salonimeena067 | 23 Dec, 2019, 11:23: AM
Expert Answer
When the object is at ∞ and moving with speed vf , total energy E(∞) of the object is as given below
E(∞) = (1/2)m vf2 + W ......................(1)
where W is potential energy at infinity
At earth surface, if the object is projected with speed vi , then total energy at earths surface is given by
E(RE) = (1/2) m vi2 - [ ( G M m )/ RE ] + W .................(2)
where G is sravitational constant , M is mass of earth and RE is radius of earth
By conservation of energy, eqn.(1) and (2) are same
Hence if we equate, eqns.(1) and (2),
(1/2)m vf2 = (1/2) m vi2 - ( G M m )/ RE
vf2 = vi2 - ( 2 G M )/ RE ...............................(3)
if we substitue given value vi = 22.4 km/s along with constants i.e., garvitational constant G,
mass of earth M and radius of earth RE , we get speed vf of object at infinity from eqn.(3)
vf = 19.41 km/s
Answered by Thiyagarajan K | 23 Dec, 2019, 03:55: PM
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