Question

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. $\frac{Gm}{\pi{l}}$along x-axis
• B. $\frac{Gm}{\pi{l}}$along y-axis
• C. $\frac{2\pi Gm}{l^{2}}$along y-axis
• D. $\frac{2\pi Gm}{l^{2}}$along x-axis

Answer 1

Answer: (C)

$\frac{2\pi Gm}{l^{2}}$along y-axis

Answer 2

Consider two small elements each of length $d l=r d \theta$ symmetrically. $\pi_{r}=1$ Resolve the elemental field intensities $\because\left|d E_{1}\right|=\left|d E_{2}\right|$