JEE MAIN - Physics (2024 - 4th April Morning Shift - No. 3)
A metal wire of uniform mass density having length $$L$$ and mass $$M$$ is bent to form a semicircular arc and a particle of mass $$\mathrm{m}$$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :
$$\frac{\mathrm{GmM} \pi^2}{\mathrm{~L}^2}$$
$$\frac{\mathrm{GMm} \pi}{2 \mathrm{~L}^2}$$
0
$$\frac{2 \mathrm{GmM} \pi}{\mathrm{L}^2}$$
Explanation
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Field at centre due to arc, $$I=\frac{2 G M \pi}{L^2}$$
$$\therefore \quad$$ Net force on mass, $$F=\frac{2 G M m \pi}{L^2}$$
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