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The velocity v of a particle (under a fo...

The velocity v of a particle (under a force F) depends on its distance (x) from the origin (with x `gt`0) v `prop = (1)/(sqrt(x))` .Find how the magnitude of the force (F) on the particle depends on x.

A

F`prop (1)/(x^(3//2))`

B

`F prop (1)/(x)`

C

`F prop (1)/(x^(2))`

D

`F prop x`

Text Solution

Verified by Experts

`v prop (1)/(sqrt(x)) or, v = (k)/(sqrt(x))`
`therefore" " (dv)/(dt) = (d)/(dx)(kx^(-(1)/(2))) (dx)/(dt) =v(d)/(dx)(kx^(-(1)/(2)))`
` = k.xx (1)/(x^(2)) [ " where " k. = (k^(2))/(2)]`
`therefore" "a prop (1)/(x^(2))`
so, `F prop (1)/(x^(2))`
The option c is correct.
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