**Solve the following problem.**

A planet has mass 6.4 × 10^{24} kg and radius 3.4 × 10^{6} m. Calculate the energy required to remove an object of mass 800 kg from the surface of the planet to infinity.

#### Solution

**Given: **M = 6.4 × 10^{24} kg, R = 3.4 × 10^{6} m, m = 800 kg

**To find:** Energy required to remove the object from the surface of planet to infinity = B.E.

**Formula: **B.E. = `"GMm"/"R"`

**Calculation:** We know that,

G = 6.67 × 10^{–11} N m^{2}/kg^{2}

From formula,

B.E. = `(6.67 xx 10^-11 xx 6.4 xx 10^24 xx 800)/(3.4 xx 10^6)`

∴ B.E. =`(6.67 xx 6.4 xx 8)/3.4 xx 10^9`

`= (6.67 xx 51.2)/3.4 xx 10^9`

= antilog{log(6.67) + log(51.2) – log(3.4)} × 10^{9}

= antilog{0.8241 + 1.7093 – 0.5315} × 10^{9}

= antilog{2.0019} × 10^{9}

= 1.004 × 10^{2} × 10^{9}

= 1.004 × 10^{11} J

Energy required to remove the object from the surface of the planet is **1.004 × 10 ^{11} J.**