Q: A bullet of mass 10gm is fired horizontally with a velocity 1000m/s from a riffle situated at a height 50m above the ground. If the bullet reaches the ground with a velocity 500m/s , the work done against air resistance in the trajectory of the bullet is (in joule) (g = 10ms^{-2})

(a) 5005

(b) 3755

(c) 3750

(d) 17.5

Ans: (b)

Sol:

work done against air resistance W_{f} = Loss in K.E + Loss in P.E

$ \displaystyle W_f = \frac{1}{2}m (1000)^2 – \frac{1}{2}m (500)^2 + m h (50) $

$ \displaystyle W_f = \frac{1}{2}10 \times 10^{-3} (1000+500)(1000-500) + 10 \times 10^{-3}\times 10 \times 50 $

W_{f} = 3755 J