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A liquid drop of mass m andradius r is f...

A liquid drop of mass m andradius r is falling from great height. Its velocity is proportional to

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`(d)/(dt) (mv) = mg , (dm)/(dt) = lambda or m = lambda t + K`
where K is a constant when t=0 , `m=m_0 :. m=m_0 + lambda t `
so , ` (d)/(dt) {(m_0 + lambda t)v} = (m_0 + lambda t ) g`
Integrating , `(m_0 + lambda t) v= int (m_0 + lambda t) g dt = (m_0 t + ( lambda t^(2))/(2) ) g + C ` where C is constant
when t =0, v=0 ` :.` C =0
`:. (m_0 + lambda t) v = ( m_0 t + ( lambda t^2)/(2)) g , v=(g(m_0 t + (lambda t^2)/( 2)))/(m_0 + lambda t ) =(g (t+ (lambdat^(2))/(2m_0)))/( 1 + (lambda t)/( m_0))`
This mean velocity changes w.r.t . time
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