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The escape velocity from the earth is 11.2km/sec. Another plant is having a mass 1000 times and radius 10 times that of the earth, then escape velocity at that planet will be

Question

The escape velocity from the earth is 11.2km/sec. Another plant is having a mass 1000 times and radius 10 times that of the earth, then escape velocity at that planet will be

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Solution

The escape velocity from a planet is given by the formula:

v = sqrt((2GM)/r)

where:

  • v is the escape velocity,
  • G is the gravitational constant,
  • M is the mass of the planet, and
  • r is the radius of the planet.

Given that the mass of the other planet is 1000 times that of Earth and the radius is 10 times that of Earth, we can substitute these values into the formula:

v = sqrt((2G1000M)/(10r))

This simplifies to:

v = sqrt((200GM)/r)

Since the escape velocity from Earth (v) is known to be 11.2 km/sec, we can substitute this into the equation:

11.2 = sqrt((200GM)/r)

Squaring both sides gives:

125.44 = (200GM)/r

Solving for the escape velocity from the other planet (v') gives:

v' = sqrt((200G1000M)/(10r))

This simplifies to:

v' = sqrt((20000GM)/r)

Substituting the known values gives:

v' = sqrt((20000*125.44)/r)

Solving this gives:

v' = sqrt(2508800/r)

Converting this to km/sec (since the radius is in km and the velocity is in km/sec) gives:

v' = sqrt(2508800)/sqrt(r)

v' = 1584 km/sec

So, the escape velocity at the other planet would be 1584 km/sec.

This problem has been solved

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