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A particle is at rest at x=a. A force ve...

A particle is at rest at `x=a`. A force `vecF=(b)/(x^(2))veci`
begins to act on the particle. The particle starts its motion, towards the origin, along X-axis. Find the velocity of the particle, when it reaches a distance x from the origin .

Text Solution

Verified by Experts

`F= - (b)/(x^(2)) rArr (d)/(dt) rArr (p) = - (b)/(x^(2))`
`(d)/(dt) (mv) = - (b)/(x^(2)) rArr m (dv)/(dx) (dx)/(dt) = - (b)/(x^(2))`
`mv dv = - (b)/(x^(2)) dx rArr vdv = - (b)/(mx^(2))dx`
`underset(0)overset(v)(int)v dv =underset(a)overset(x)int - (b)/(mx^(2)) dx rArr(v^(2))/(2)=(b)/(m)[(1)/(x)]_(a)^(x)`
`(v^(2))/(2) = (b)/(m) [1/(x)-(1)/(a)]:.u = sqrt((2b)/(m)((a-x)/(xa)))` .
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