A particle falls from infinity to the earth. Its velocity on reaching the earth surface will be
Answers
According to me , your question is -------> find velocity of particle when particle falls towards earth from infinity ?
We know, Total energy = kinetic energy + potential energy [ when external energy is neglected ]
kinetic energy of particle at earth surface = 1/2mv²
Here, m is mass of particle and v is velocity of particle at Earth's surface.
potential energy of particle = -GMm/r
Here, M is mass of earth and r is the radius of earth.
Totol energy of particle at infinity = 0
∴ 0 = 1/2mv² - GMm/r
⇒1/2 mv² = GMm/r
⇒v² = 2GM/r
⇒v = √{2GM/r}
Here, G = 6.67 × 10⁻¹¹ Nm²/kg²
M = 6 × 10²⁴ kg
r = 6400 km = 6.4 × 10⁶ m
∴ v = √{2 × 6.67 × 10⁻¹¹ × 6 × 10²⁴/6.4 × 10⁶}
= √{2 × 6.67 × 6 × 10⁷/6.4}
= √{2 × 66.7 × 6/6.4} × 10³ m/s
≈ 11 km/s
Hence, velocity of particle at earth surface is 11 km/s
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Answer:
1/2mv exp 2 - GMm/R=0
Explanation:
It will be exactly equal to the escape velocity on the surface of the Earth. When the body is at infinity and it's velocity is 0,it's potential as well as kinetic velocity is 0. So the total Energy is 0.
When it reaches the surface of the Earth, it's kinetic energy is 1/2mv exp 2. The potential energy is - GMm/R. Therefore, 1/2mv exp 2=0