The period of a simple pendulum of length 80.0cm was found to have doubled when the length of the pendulum was increased by X. Calculate X.
Question 1 Report
The period of a simple pendulum of length 80.0cm was found to have doubled when the length of the pendulum was increased by X. Calculate X.
Answer Details
The period of a simple pendulum depends on its length. The relationship between the period (T) of a simple pendulum and its length (L) is given by the formula: T = 2π√(L/g), where g is the acceleration due to gravity. If the period of the pendulum doubles, then the new period (T') is twice the original period (T): T' = 2T = 4π√(L/g). If the length of the pendulum is increased by X, then the new length (L') is: L' = L + X. Substituting this into the formula for the new period gives: T' = 2π√((L+X)/g) Since T' = 2T, we can equate the two expressions for T' and simplify: 4π√(L/g) = 2π√((L+X)/g) Squaring both sides and canceling the common factor of 4π2/g, we get: L = (L+X)/2 Solving for X gives: X = L Therefore, the length of the pendulum needs to be increased by 80.0 cm to double its period, so X = 80.0 cm. The answer is option D: 240.0 cm.
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