A rain drop falling vertically under gravity gathers moisture from the atmosphere at a rate dm given by. kt2, where mn is the instantaneous mass, t is time and k is a constant. The dt %3D dv equation of motion of the rain drop is m- dt dm = mg dt If the drop starts falling at t=0, with zero initial velocity and initial mass m ( m, = 2 gm, k =12 gm/s' and g =1000 cm/s), the velocity v of the drop after one second is (a) 250 cm/s (b) 500 cm/s (c) 750 cm/s (d) 1000 cm/s

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Q13. A rain drop falling vertically under gravity gathers moisture from the atmosphere at a rate
given by
am = kt?, where m is the instantaneous mass, t is time and k is a constant. The
dt
dv
equation of motion of the rain drop is m
dm
+ v
dt
= mg
dt
If the drop starts falling at t=0, with zero initial velocity and initial mass m,
(m, = 2 gm, k =12 gm/s' and g =1000 cm/s ), the velocity v of the drop after one
second is
(а) 250 ст/ s
(b) 500 ст/ s
(с) 750 ст/ s
(d) 1000 ст/ s
Transcribed Image Text:Q13. A rain drop falling vertically under gravity gathers moisture from the atmosphere at a rate given by am = kt?, where m is the instantaneous mass, t is time and k is a constant. The dt dv equation of motion of the rain drop is m dm + v dt = mg dt If the drop starts falling at t=0, with zero initial velocity and initial mass m, (m, = 2 gm, k =12 gm/s' and g =1000 cm/s ), the velocity v of the drop after one second is (а) 250 ст/ s (b) 500 ст/ s (с) 750 ст/ s (d) 1000 ст/ s
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