JEE Main 2021 · 22 July · evening · Single correct · +4 / −1
T₀ is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to 1/16 times of its initial value, the modified time period is :
- (a) 4 T₀
- (b) 1/4 T₀
- (c) T₀
- (d) 8π T₀
Answer and solution
Answer (b) 1/4 T₀
Solution
Physics sir · 2 steps
The period goes as the square root of length, so a 16 times shorter string ticks 4 times faster.
- Period formula. For a simple pendulum, T = 2π√(L/g). At the same place g does not change, so T ∝ √L.
T/T₀ = √((L/16)/L) = √(1/16) = 1/4
- So. The new period is 1/4T₀, which is option (b).
The idea to keep. Since T ∝ √L, scaling the length by any factor scales the period by the square root of that factor. Take the root before you scale.
Answer from the NTA final answer key. Solution by PrepWiser.