A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M of amplitude 10 cm . The maximum tension in the string is found to be x 40 N . The value of x is _____.

Step-by-step solution

From the given figure we can see that sin θ 0 = A l = 10 100 = 1 10 From conservation of energy m v 2 2 = m g l ( 1 - cos θ 0 ) Maximum tension occurs at mean position T = m g + m v 2 l ⇒ T = m g + 2 m g ( 1 - cos θ 0 ) Substituting the values, T = m g ( 1 + 2 ( 1 - 1 - sin 2 θ 0 ) ⇒ T = m g ( 3 - 2 1 - 1 100 ) ⇒ T = 0 . 25 × 9 . 8 ( 3 - 2 ( 1 - 1 200 ) ) ⇒ T = 0 . 25 × 9 . 8 × 1 . 01 = 2 . 4745   N It is given that T = x 40 ⇒ x = 40 × 2 . 4