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A railway carriage of mass M(c) filled w...

A railway carriage of mass `M_(c)` filled with sand of mass `M_(s)` moves along the rails. The carriage is given an impulse and it starts with a velocity `v_(0)`. At the same time it is observed that the sand starts leaking through a hole at the bottom of the carriage at a constant mass rate `lambda`. Find the distance at which the carriage becomes empty and the velocity attained by the carriage at that time. (Neglect the friction along the rails).

Text Solution

Verified by Experts


At `t`,
`t=0`

`F=m(dt)/(dt)+(v+v_(0))(dm)/(dt)`
`0+m(dv)/(dt)+(v+v_(0))(dm)/(dt)`
`rArr (dv)/(dt)=0`
`rArr v=` constant
`rArr v=v_(0)` Ans.
Also `S=v_(0)t`
`S=V_(0)(M_(s))/(lambda)Ans.`
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