A body of mass 10 kg is dropped from a height of 10 m on a planet, whose mass and radius are double that of the earth. find the maximum kinetic energy the body can posses
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In this question, we need to find the (g) acceleration due to gravity of the planet,
g= (GM)/R² (where M and R are the Mass and Radius of the planet and G is gravitational constant)
Case-1) At earth,
g₁ = (Gm₁)/r₁² = 10m/s² apx.
Case-2) At another planet whose m₂=2m₁ and r₂=2r₁
g₂ = (Gm₂)/r₂²
g₂ = (G(2m₁))/(2r₁²)
g₂ = 2(Gm₁)/4r₁²
g₂ = (Gm₁)/2r₁²
g₂ = g₁(1/2) = 5m/s² apx
(Maximum kinetic energy= total mechanical energy)
since velocity of the body is nil(0), so
total mechanical energy= its potential energy
Hence,
KE |max| = mg₂h
KE |max| = (10)(5)(10)
KE |max| = 500J
Hope it helps!
g= (GM)/R² (where M and R are the Mass and Radius of the planet and G is gravitational constant)
Case-1) At earth,
g₁ = (Gm₁)/r₁² = 10m/s² apx.
Case-2) At another planet whose m₂=2m₁ and r₂=2r₁
g₂ = (Gm₂)/r₂²
g₂ = (G(2m₁))/(2r₁²)
g₂ = 2(Gm₁)/4r₁²
g₂ = (Gm₁)/2r₁²
g₂ = g₁(1/2) = 5m/s² apx
(Maximum kinetic energy= total mechanical energy)
since velocity of the body is nil(0), so
total mechanical energy= its potential energy
Hence,
KE |max| = mg₂h
KE |max| = (10)(5)(10)
KE |max| = 500J
Hope it helps!
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