A 1 kg particle moves at constant speed 1 m/s along y=0.5 cos(2πx/ℓ), ℓ=1 m. At lowest point B, normal force is 5n N. Given π²=g=10 m/s², find n.
Physics · Mixed Chapter
JEE Main Practice

Question

A 1 kg particle moves at constant speed 1 m/s along y=0.5 cos(2πx/ℓ), ℓ=1 m. At lowest point B, normal force is 5n N. Given π²=g=10 m/s², find n.

G1 Physics · Accepted Answer

Step 1: At the trough, y′=0; y″=−0.5(2π/ℓ)² cos(2πx/ℓ)=+2π² m⁻¹. Step 2: The local radius of curvature is R=1/|y″|=1/(2π²) m. Step 3: Centripetal acceleration v²/R=2π²=20 m/s² upward. Step 4: N−mg=mv²/R ⇒N=10+20=30 N=5n N. Thus n=6.