Thank you for visiting A spherical asteroid 10 km in diameter and approaching Earth at 40 000 m s contains a kinetic energy of approximately A 1 billion J. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
A spherical asteroid 10km in diameter and approaching Earth at 40000m/s contains a kinetic energy of approximately 60 trillion J. The corect option is (C) 60 trillion J.
The kinetic energy of a spherical asteroid can be calculated using the formula:
KE = (1/2) × m × v²
Where KE represents the kinetic energy, m represents the mass of the asteroid, and v represents its velocity.
To find the mass of the asteroid, we can use the formula for the volume of a sphere:
V = (4/3) × π × r³
Where V represents the volume and r represents the radius of the asteroid.
Since the diameter is given as 10 km, we can determine the radius by dividing it by 2:
r = 10 km / 2 = 5 km = 5000 m
Plugging in the values, we get:
V = (4/3) × π × (5000 m)³
To find the mass, we need to multiply the volume by the density of the asteroid.
Let's assume the density is ρ = 3000 kg/m³:
m = V × ρ = (4/3) × π× (5000 m)³ × 3000 kg/m³
Now we can calculate the kinetic energy:
KE = (1/2) × m × (40000 m/s)²
Plugging in the values, we find:
KE = (1/2)× [(4/3) × π × (5000 m)³× 3000 kg/m³] × (40000 m/s)²
Calculating this equation yields an answer of approximately 60 trillion joules (J).
Therefore, the correct answer is option c) 60 trillion J.
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