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A wire of length l and mass m is bent in...

A wire of length l and mass m is bent in the form of a semicircle. The gravitational field intensity at the centre of semicircle is

A

`(Gm)/(pil)` along x- axis

B

`(Gm)/(pil)` along y-axis

C

`(2pGm)/(l^(2))` along y-axis

D

`(2piGm)/(l^(2))` along x-axis

Text Solution

Verified by Experts

The correct Answer is:
C
Consider two small elements each of length `dl=r d theta` symmetrically.
`pir=l`
Resolve the elemental field intensites
`because |dE_(1)|=|dE_(2)|`

`dE=2dE_(1) cos theta=(2Grd theta)/(r^(2))cos theta`
G = Gravitational constant
`lambda `=Linear mass density `=(m)/(l)`
or `dE=(2lambdaG)/(r)int_(0)^(90^(@))cos theta d theta =(2lambdaG)/(r)=(2piGm)/(l^(2))`
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