A uniform wire bent in the form of a semicircle is suspended about a horizontal axis passing through one of its ends and normal to its plane so that it can swing in the vertical plane. In equilibrium the line joining the ends makes an angle θ = tan⁻¹(n/π) with vertical. The value of n is ...
Physics · Mixed Chapter
JEE Mains

Question

A uniform wire bent in the form of a semicircle is suspended about a horizontal axis passing through one of its ends and normal to its plane so that it can swing in the vertical plane. In equilibrium the line joining the ends makes an angle θ = tan⁻¹(n/π) with vertical. The value of n is ...

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The centre of mass of a uniform semicircular wire is at distance 2R/π from the circle centre along the axis of symmetry. Step 2: Taking the top end as pivot, the centre of mass lies R below the centre in its original orientation and 2R/π sideways. At equilibrium its position vector from pivot is vertical. Step 3: The angle between the diameter and vertical therefore satisfies tanθ=(2R/π)/R=2/π. Step 4: θ=tan⁻¹(n/π), so n=2.