The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is

The time period of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.

Step 1: Understand the problem The length of the pendulum is increased by 21%, and we need to find the percentage increase in the time period.

Step 2: Apply the percentage increase to the length If the original length is L, the new length L' is L + 0.21L = 1.21L.

Step 3: Find the new time period The new time period T' is given by T' = 2π√(L'/g) = 2π√(1.21L/g).

Step 4: Express the new time period in terms of the old time period We can write T' = T√(1.21), since T = 2π√(L/g).

Step 5: Find the percentage increase in the time period The percentage increase is given by ((T' - T) / T) * 100%. Substituting T' = T√(1.21) gives ((T√(1.21) - T) / T) * 100% = (T(√(1.21) - 1) / T) * 100% = (√(1.21) - 1) * 100%.

So, the percentage increase in the time period of the pendulum of increased length is approximately 10%.