Question

The earth circles around the sun once a year. The work which would have to be done on the earth to bring it to rest relative to the sun is, (Ignore the rotation of earth about its own axis) given that the mass of the earth $=6 \times 10^{24}\, kg$ and distance between sun and earth is $1.5 \times 10^{8}\, km$)

• A. $2.7 \times {10}^{30}\,J$
• B. $2.7\times {10}^{31}\, J$
• C. $-2.7\times {10}^{33}\, J$
• D. $+2.7 \times {10}^{33}\, J$

Answer 1

Answer: (C)

$-2.7\times {10}^{33}\, J$

Answer 2

$\omega =\frac{2 \pi}{T}$ $=\frac{2 \pi}{365 \times 24 \times 3600}$ $=1.99 \times 10^{-7}\, rad / s$ $W =K_{f}-K_{i}=0-\frac{1}{2} m v^{2}$ $(v=\omega R)$ $=\frac{1}{2} \times 6 \times 10^{24} \times\left(1.5 \times 10^{11} \times 1.99 \times 10^{-7}\right)^{2}$ $=-2.7 \times 10^{33}\, J$