A `1 kg` mass is projected down a rough circule track `(redius = 2.0 m)` placed in vertical plane as shown. The speed of the mass at point `A` is `3 m//s` and at point `B`, it is `6.0 m//s`. How much is work is done on the mass between `A` and `B` by the force of friction?

Options

A. `-7.5 J`
B. `-8.5 J`
C. `-6.5 J`
D. `-24 J`

Answer

C

Explanation

Conservation of energy principal
`KE` = at `A = (1)/(2) xx 1.0 xx 3.0^(2) = 4.5 J`
Loss in `PE` between `A` and `B = 1.0 xx 10 xx 2 = 20J`
Gain in `KE` from `A` to `B` if there had been no friction = `20 J`
total `KE` at `B` if there had been no friction
`= 4.5 + 20 = 24.5 J`
Los in energy due to friction `= 24.5 - 18 =m 6.5 J`.