A uniform hemispherical shell placed on an inclined plane of inclination θ is at rest. The angle made by the circular face of the shell with horizontal is φ = sin⁻¹(n sinθ). The value of n is ...
Physics · Mixed Chapter
JEE Mains

Question

A uniform hemispherical shell placed on an inclined plane of inclination θ is at rest. The angle made by the circular face of the shell with horizontal is φ = sin⁻¹(n sinθ). The value of n is ...

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: For a thin uniform hemispherical shell, the centre of mass lies R/2 from the sphere centre along its symmetry axis. Step 2: In static equilibrium the weight passes vertically through the contact point with the incline. The sphere centre is R along the incline's normal from this contact, so the contact point's horizontal offset relative to the centre is R sinθ. Step 3: The centre of mass has horizontal offset (R/2)sinφ relative to the sphere centre when its circular face makes angle φ to…