Answer to Question #105608 in Classical Mechanics for Panops

Question

Ceres is the largest asteroid. Its mean radius is }476 km and its mass is 9.4×10^20 kg. Using this, and G = 6.67×10^ −11 Nm^2 kg^ −2, and approximating it as a sphere, compute the speed required to escape the gravity on the surface of Ceres.

Speed= ___ m/s . (to two significant figures, don't use scientific notation)

Answer 1

As per the given question,

Mean radius of asteroid =476km

mass$=9.4\times 10^{20}kg$

$G = 6.67×10^{ −11} Nm^2 kg^ {−2}$

Now, applying conservation of energy,

$\dfrac{GMm}{r}=\dfrac{mV^2}{2}$

$V=\sqrt{\dfrac{2GM}{r}}$

$V=\sqrt{\dfrac{2\times 6.67\times 10^{-11}\times9.4\times10^{20}}{476\times10^{3}}}$

$V=\sqrt{\dfrac{125.396\times10^9}{476\times 10^3}}$

$V=\sqrt{0.263\times 10^6} m/sec$

$V=0.5\times 10^3 m/sec$

$V=0.5 km/sec$