A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

11

21

31

41

A car loaded with water (total mass 1000 kg) moves on a horizontal road from rest under a constant horizontal force F = 100 N.
Water spills through a small hole at the rate 0.1 kg/s. Find the velocity after 300 s.

Given:
Initial mass m0 = 1000 kg
Leak rate = 0.1 kg/s
F = 100 N
Time t = 300 s

Assumption: water leaves vertically (no horizontal relative velocity), so horizontal momentum equation reduces to
m(t) dv/dt = F.

Mass as a function of time:
m(t) = 1000 − 0.1 t

So
v = ∫[0→300] F / m(t) dt = ∫[0→300] 100 / (1000 − 0.1 t) dt

Let m = 1000 − 0.1 t ⇒ dm = −0.1 dt ⇒ dt = −10 dm
When t = 0, m = 1000; when t = 300, m = 970

v = 100 ∫{t=0}^{300} dt / (1000 − 0.1 t)
= 100 ∫{m=1000}^{970} (−10 dm) / m
= 1000 ∫_{970}^{1000} dm / m
= 1000 ln(1000 / 970)

Numerical value:
ln(1000/970) ≈ 0.03044
v ≈ 1000 × 0.03044 ≈ 30.44 m/s

Nearest choice: 31

Final answer: 31 (velocity ≈ 30.44 m/s)