This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's the solution for question 37. Step 1: Identify the formula for the period of a simple pendulum. The period T of a simple pendulum is given by the formula: T = 2 sqrt((L)/(g)) where L is the length of the pendulum and g is the acceleration due to gravity. Step 2: Set up the ratio of the periods for the two cases. Let T_1 be the initial period and L_1 be the initial length. Let T_2 be the new period and L_2 be the new length. We have: T_1 = 2 sqrt((L_1)/(g)) T_2 = 2 sqrt((L_2)/(g)) Dividing the second equation by the first gives: (T_2)/(T_1) = (2 sqrt(L_2)/(g))2 sqrt((L_1)/(g)) = sqrt((L_2)/(L_1)) Step 3: Substitute the given values and solve for L_2. Given: T_1 = 62 s, L_1 = 40 cm, T_2 = 72 s. We need to find L_2. (72)/(62) = sqrt((L_2)/(40)) Square both sides: ((72)/(62))^2 = (L_2)/(40) L_2 = 40 × ((72)/(62))^2 L_2 = 40 × (1.16129)^2 L_2 = 40 × 1.34859 L_2 ≈ 53.94 cm Step 4: Calculate the increase in length, X. The length is increased by X, so L_2 = L_1 + X. X = L_2 - L_1 X = 53.94 cm - 40 cm X = 13.94 cm Step 5: Compare with the given options. The calculated value X ≈ 13.9 cm matches option A. The final answer is A. 13.9 cm. Send me the next one 📸