A rain drop of mass m_(0) starts falling from rest and it collects water vapour and grows . If it gains lambda kg//s,find its velocity at any instant.

A rain drop of mass m_(0) starts falling from rest and it collects wat

1.	A rain drop of mass m_(0) starts falling from rest and it collects water vapour and grows . If it gains lambda kg//s,find its velocity at any instant.
Answer» <html><body><p></p>Solution :`d/(dt) (<a href="https://interviewquestions.tuteehub.com/tag/mv-1082193" style="font-weight:bold;" target="_blank" title="Click to know more about MV">MV</a>) =<a href="https://interviewquestions.tuteehub.com/tag/mg-1095425" style="font-weight:bold;" target="_blank" title="Click to know more about MG">MG</a>,(<a href="https://interviewquestions.tuteehub.com/tag/dm-432223" style="font-weight:bold;" target="_blank" title="Click to know more about DM">DM</a>)/(dt)=lambda "or" m=lambdat+K`<br/>where K is a constant when `t=0, m=m_(0) :. M=m_(0)+lambdat`<br/>so,`d/(dt){(m_(0)+lambdat)v}=(m_(0)+lambdat)<a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a>`<br/> Integrating, `(m_(0)+lambdat)v=int(m_(0)+lambdat)gdt =(m_(0)t+(lambdat^(2))/2)g+C ` where c is a constant <br/> when `t=0, v=0``:. C=0`<br/> `:. (m_(0)+lambdat) v=(m_(0)t+(lambdat^(2))/2)g , v =(g(m_(0)t+(lambdat^(2))/2)/(m_(0)+lambdat)=(g(t+(lambdat^(2))/(2m_(0))/(1+(lambdat)/m_(0)))`<br/> Thismean velocitychanges w.r.t.time</body></html>