A simple pendulum of length 100 cm and bob mass 250 g executes SHM of amplitude 10 cm. The maximum tension in the string is (x/40) N. The value of x is ______.
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 2 Evening Shift

Question

A simple pendulum of length 100 cm and bob mass 250 g executes SHM of amplitude 10 cm. The maximum tension in the string is (x/40) N. The value of x is ______.

G1 Physics · Accepted Answer

For a simple pendulum of length l with small amplitude A: ω² = g/l At the mean position, speed is maximum: v(max) = ωA Maximum tension: T(max) = mg + mv(max)²/l = mg + m(ω²A²)/l = mg[1 + A²/l²] Given: m = 0.25 kg l = 1.0 m A = 0.10 m g = 9.8 m s⁻² T(max) = 0.25×9.8×(1 + 0.01) ≈ 2.4745 N Given T(max) = x/40 N: x = 40×2.4745 ≈ 99 Final value: 99