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A particle of mass m is allowed to oscil...

A particle of mass `m` is allowed to oscillate near the minimum of a vertical parabolic path having the equaiton `x^(2) =4ay`. The angular frequency of small oscillation is given by

A

`sqrt(gh)`

B

`sqrt(2gh)`

C

`sqrt(((g)/(2a)))`

D

`sqrt(((g)/(a)))`

Text Solution

Verified by Experts

The correct Answer is:
C
At the vertex, tangential acceleration is zero. When particle is at mean position, it is at vertex. When it is displaced for small angle `theta`,
`-mf=mg sin theta`
or `f=-g sin theta=-g theta tan theta`
or `f=-g((dt)/(dx))`
`because" "x^(2)=4ay or 2x =42(dy)/(dx)`
`or" " (dy)/(dx)=(x)/(2a)therefore tantheta=(x)/(2a)`

`therefore" "f=-g((x)/(2a))`
or `-omega^(2)x=-g((x)/(2a))`
`therefore" "omega=sqrt(((g)/(2a)))`
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