Question

In the solar system, the Sun is in the focus of the ellipse for Sun-earth binding system. The binding energy for the system will be $($Given that radius of the earth's orbit around the Sun is $1.5\times {10}^{11}\text{m}$, mass of the earth is $6\times {10}^{24}\text{kg}$, mass of the Sun is $6\times {10}^{30}\text{kg}$, and $G=6.67\times {10}^{-11}{\text{Nm}}^2/$${\text{kg}}^2)$

• A. $2.7\times {10}^{33}\text{J}$
  
• B. $5.4\times {10}^{33}\text{J}$
• C. $2.7\times {10}^{23}\text{J}$
• D. $5.4\times {10}^{32}\text{J}$

Answer 1

The correct option is A $2.7\times {10}^{33}\text{J}$


The binding energy of a star-planet system is given by,
$$\text{B.E =}-\text{Total mechanical energy}=\frac{GMm}{2R}...\left(1\right)$$ Given,
Mass of the sun, $M=6\times {10}^{30}\text{kg}$,

$G=6.67\times {10}^{-11}{\text{Nm}}^2/{\text{kg}}^2$

Mass of the earth, $m=6\times {10}^{24}\text{kg}$

Radius of the orbit, $R=1.5\times {10}^{11}\text{m}$

$\text{B.E}=\frac{(6.67\times {10}^{-11})\times (6\times {10}^{30})\times (6\times {10}^{24})}{2\times 1.5\times {10}^{11}}$

$\Rightarrow \text{B.E}=2.7\times {10}^{33}\text{J}$

Hence, option (a) is the correct answer.

Why this question: To make students understand the concept of binding energy and its relationship with total mechanical energy of the system.