A uniform rope of mass 2 kg and length 3 m rotates in a horizontal plane about one end with angular speed 4 rad/s. If the maximum tension in the rope is N newton, find N.
Physics · Circular Motion · centripital force and centrifugal force
JEE Mains NEET JEE Advanced

Question

A uniform rope of mass 2 kg and length 3 m rotates in a horizontal plane about one end with angular speed 4 rad/s. If the maximum tension in the rope is N newton, find N.

G1 Physics · Accepted Answer

For a massive radial rope, T(x) = Mω²(R² − x²)/(2R). Maximum tension occurs at the fixed end, x=0. Hence T_max = Mω²R/2 = 2×4²×3/2 = 2×16×3/2 = 48 N. Therefore N=48.