A body is moving under the acton of central force `vrc(F)(r ) hat(e )`. Then, choose the correct statement (symbols are having usual meaning and `hat(e ), hat(e )`, denote unit vectors along the radial and tangential direction, respectively ) from the following.

Options

A. `vec(v) = (dr)/(dt) hat(e)_(r ) + r(d theta)/(dt) hat(e)_(theta), vec(a) = [(d^(2)r)/(dt^(2)) - r ((d theta)/(dt))^(2)] hat(e)_(r ), 2(dr)/(dt) (d theta)/(dt) + r (d^(2)theta)/(dt^(2)) = 0`
B. `vec(v) = (dr)/(dt) hat(e)_(r ) + r(d theta)/(dt) hat(e)_(theta), vec(a) = [(d^(2)r)/(dt^(2)) + r ((d theta)/(dt))^(2)] hat(e)_(r ), 2(dr)/(dt) (d theta)/(dt) - r (d^(2)theta)/(dt^(2)) = 0`
C. `vec(v) = (dr)/(dt) hat(e)_(r ) - r(d theta)/(dt) hat(e)_(theta), vec(a) = [(d^(2)r)/(dt^(2)) + r ((d theta)/(dt))^(2)] hat(e)_(r ), 2(dr)/(dt) (d theta)/(dt) + r (d^(2)theta)/(dt^(2)) = 0`
D. `vec(v) = (dr)/(dt) hat(e)_(r ) - r(d theta)/(dt) hat(e)_(theta), vec(a) = [(d^(2)r)/(dt^(2)) - r ((d theta)/(dt))^(2)] hat(e)_(r ), 2(dr)/(dt) (d theta)/(dt) + r (d^(2)theta)/(dt^(2)) = 0`

Answer

A

Explanation

Use `(dhat(e)_(r ))/(dt) = (d theta)/(dt) hat(e)_(theta)`. and `(dhat(e)_(theta))/(dt) = -(dtheta)/(dt) hat(e)_(r )`