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BIOLOGYThe work required to launch an object from the surface of Earth to outer space is given by W=$\int _ { R } ^ { \infty } F ( x ) d x$, where R=6370 km is the approximate radius of Earth, F(x)=$G M m / x ^ { 2 }$ is the gravitational force between Earth and the object, G is the gravitational constant, M is the mass of Earth, m is the mass of the object, and GM=$4 \times 10 ^ { 14 } \mathrm { m } ^ { 3 } / \mathrm { s } ^ { 2 }$. a. Find the work required to launch an object in terms of m. b. What escape velocity $v_e$ is required to give the object a kinetic energy $\frac { 1 } { 2 } m v _ { e } ^ { 2 }$ equal to W? c. The French scientist Laplace anticipated the existence of black holes in the 18th century with the following argument: If a body has an escape velocity that equals or exceeds the speed of light, c=300,000 km/s, then light cannot escape the body and it cannot be seen. Show that such a body has a radius R$\leq 2 G M / c ^ { 2 }$. For Earth to be a black hole, what would its radius need to be?