If the length of a simple pendulum is increases by 1percent, then the new time-period
a) Decreases by 0.5 percent
b) Increases by 0.5 percent
c) Increases by 1 percent
d) Increases by 2.0 percent
Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Time period, T=2π√l/g
=>T∝√l
=>ΔT/T=1/2 Δl/l
Δl/l=1%
Therefore, ΔT/T=1/2x1%=0.5%

Answer

Answer should be c

Answer

Time period, T=2π√l/g
=>T∝√l
=>ΔT/T=1/2 Δl/l
Δl/l=1%
Therefore, ΔT/T=1/2x1%=0.5%

Answer

If the length is increased by 1% then the new length will be 101/100 L and the formula of tome period of pendulum is 2π√l/g squaring both sides we get T^=4π^l/g now putting new length in the forumla new length -  original lenth whole devided by original length *100 we will get pur knew length

Answer

Effects of Increasing the Length of a Simple Pendulum on the Time Period

Introduction:
A simple pendulum consists of a mass (bob) attached to a string or rod of fixed length. When the pendulum is displaced from its equilibrium position and released, it oscillates back and forth. The time taken for one complete oscillation is called the time period of the pendulum.

In this question, we are given that the length of the simple pendulum is increased by 1 percent and we need to determine the effect on the time period.

Understanding the Relationship:
The time period of a simple pendulum is directly related to its length. According to the formula for the time period of a simple pendulum:

T = 2π√(L/g)

Where:
T = Time period
L = Length of the pendulum
g = Acceleration due to gravity (approximately 9.8 m/s^2)

Analysis:
Let's assume the original length of the pendulum is L, and the new length is L'. We are given that L' = L + 1% of L, which can be written as L' = L + 0.01L.

Substituting this value in the formula for the time period, we get:

T' = 2π√((L + 0.01L)/g)
= 2π√(1.01L/g)
= 2π * √(1.01) * √(L/g)
= 2π * √(1.01) * T

Conclusion:
From the analysis, it is clear that the new time period T' is equal to the original time period T multiplied by the square root of 1.01. Since the square root of 1.01 is slightly greater than 1, the new time period T' is slightly greater than the original time period T.

Therefore, if the length of a simple pendulum is increased by 1 percent, the new time period increases by approximately 0.5 percent.

The correct answer is option B) Increases by 0.5 percent.

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