A solid hemisphere of radius r and mass M is pulled by means of a string (figure) so that it moves with a uniform velocity. If μ is the coefficient of friction with the surface, then the angle of inclination of the circular face of the hemisphere with the horizontal is given by sinθ = 8μ/(n+8μ). Find n = ?
Physics · Mixed Chapter
JEE Mains

Question

A solid hemisphere of radius r and mass M is pulled by means of a string (figure) so that it moves with a uniform velocity. If μ is the coefficient of friction with the surface, then the angle of inclination of the circular face of the hemisphere with the horizontal is given by sinθ = 8μ/(n+8μ). Find n = ?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Use the centroid of a solid hemisphere, which lies 3r/8 from the sphere centre towards the flat face. Step 2: For steady translation, horizontal pull equals limiting friction μN and normal N balances weight Mg. With zero angular acceleration, take torques about the instantaneous floor contact. Step 3: Substituting the 3r/8 centre-of-mass offset into the moment balance and resolving the inclined flat face gives sinθ=8μ/(3+8μ). Step 4: Comparing with 8μ/(n+8μ) yields n=3. The detailed lev…