A planet is revolving in an elliptical orbit around the sun as shown in the figure. The areal velocity (area swapped by the radius vector with respect to sun in unit time) is:

Options

A. `1/4r_(2)v_(2)`
B. `1/2v_(1)v_(1)`
C. `1/2(v_(1)r_(1)^(2))/(r_(2))`
D. dependent on the position of planet from sun

Answer

B

Explanation

As per Kepler's law, real velocity remain constant
`(dA)/(dt)=J/(2m)=(mv_(1)r_(1))/(2m)=1/2r_(1)v_(1)=1/2r_(2)v_(2)`