If the Earth were made of wood, the mass of wooden Earth would have been 10% as much as it is now (without change in its diameter). Calculate escape speed from the surface of this Earth. - Physics

Sum

Answer the following question in detail.

If the Earth were made of wood, the mass of wooden Earth would have been 10% as much as it is now (without change in its diameter). Calculate escape speed from the surface of this Earth.

Solution

Given: Mw = 10% of  M = "M"/10, Dw = D or Rw = R,

To find: Escape speed (ve)

Formula: "v"_e = sqrt((2"GM")/"R")

Calculation:

From formula,

"v"_("e"_"w") = sqrt((2"GM"_"w")/("R"_"w"))

∴ "v"_("e"_"w")/"v"_"e" = sqrt((2"GM"_"w")/("R"_"w") xx ("R")/(2"GM"))

∴ "v"_("e"_"w")/"v"_"e" = sqrt((("R")/("R"_"w")) xx (("M"_"w")/("M")))

∴ "v"_("e"_"w")/"v"_"e" = sqrt(1 xx 1/10) = sqrt(1/10)

∴ "v"_("e"_"w") = "v"_"e" xx 1/sqrt10

As, we know that the escape speed from surface of the Earth is 11.2 km/s,

Substituting value of ve = 11.2 km/s

"v"_("e"_"w") = 11.2 xx 1/sqrt10 = 11.2/3.162

= 11.2 xx 1/3.1620     ....[Taking square root value]

= antilog{log(11.2) - log(3.162)}

= antilog{1.0492 - 0.5000}

= antilog{0.5492}

= 3.542

∴ "v"_("e"_"w") = 3.54 km/s

The escape velocity from the surface of wooden Earth is 3.54 km/s.

Concept: Gravitational Potential and Potential Energy
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Balbharati Physics 11th Standard Maharashtra State Board
Chapter 5 Gravitation
Exercises | Q 4. (ii) | Page 98