The acceleration due to gravity is found up to an accuracy of 4 % on a planet. The energy supplied to a simple pendulum of known mass m to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3 % , the accuracy to which E is known as ________ %

Step-by-step solution

T = 2 π l g Δ l l × 100 = Δ g g × 100 + 2 Δ T T × 100 ⇒ Δ l l × 100 = 4 + 2 × 3 = 10 % E = 1 2 m ω 2 A 2 = 1 2 m g l A 2 Therefore ,   Δ E E × 100 = Δ g g × 100 + Δ l l × 100 = 4 + 10 = 14 %