Question

A planet revolves about the sun in elliptical orbit. The arial velocity `((dA)/(dt))` of the planet is `4.0xx10^(16) m^(2)//s`. The least distance between planet and the sun is `2xx10^(12) m`. Then the maximum speed of the planet in `km//s` is -
A. 10
B. 20
C. 40
D. None of these

Answer 1

Correct Answer - C
`(dA)/(dt) = (r^(2)omega)/(2)` is constant
`therefore (dA)/(dt) = (r_(max)^(2)omega_(min))/(2)=(r_(min)^(2)omega_(max))/(2)`
`rArr omega_(min) = (2dA//dt)/(r_(max)^(2))`
`V_(max)=omega_(min)r_(min)=(2dA//dt)/(r_(min))=40k m//s`