A particle of mass `m` is projected at an angle `alpha` to the horizontal with an initial velocity `u`. The work done by gravity during the time it reaches its highest point is

Options

A. `u^(2) sin^(2) alpha`
B. `(m u^(2) cos^(2) alpha)/(2)`
C. `(m u^(2) sin^(2) alpha)/(2)`
D. ` - (m u^(2) sin^(2) alpha)/(2)`

Answer

D

Explanation

Velocity at top `= u cos alpha`
`W_(m) = DeltaKE = (1)/(2) m(u cos alpha)^(2) -(1)/(2) m u^(2) = -(m u^(2) sin^(2) alpha)/(2)`.