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A cylindrical solid of mass 10^(-2) kg a...

A cylindrical solid of mass `10^(-2) kg` and cross-sectional area `10^(-4) m^(2)` is moving parallel to its axis (the x-axis ) with a uniform speed of `10^(3) m//s` in the positive direction. At `t = 0`, its front face passes the plane `x = 0`. The region to the right of htis plane is filled with the dust particle of uniform density `10^(-3) kg/m^(3)`. When a dust particles collides with the face of the cylinder, it stricks to its surface. Assuming that the dimensions of the cylinder remain parctically unchanged adn that the dust sticks only to the front face of the cylinder find the x-coordinate of the front of th ecylinder at `t = 150 s`.

Text Solution

Verified by Experts

The correct Answer is:
`10^(5) m`
`COLM rArr m u = (m + rho A x)v rArr v = (m u)/(m + rhoAx)`
`rArr (dx)/(dt) = (m u)/(m + rhoAx) rArr underset(0)overset(150)int (m + rhoAx)dx = underset(0)overset(150)int m u dt`
`rArr (mx + rho(Ax^(2))/(2)) = m ut`
`rArr 10^(-2) x + 10^(-3) xx (10^(-4))/(2)x^(2) = 10^(-2) xx 10^(3) xx 150 x = 10^(5) m`
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