Time period T of a simple pendulum of length l is given by T=2π√(l/g). If the length is increased by 2 %, then an approximate change in the time period is

Question

Time period T of a simple pendulum of length l is given by T=2π√(l/g). If the length is increased by 2 %, then an approximate change in the time period is (A) 2 % (B) 1 % (C) (1/2) % (D) None of these

Tardigrade Admin · Accepted Answer

(dT/dℓ)=(2π/√g). (1/2√ℓ) ∴ Δ T=(dT/dℓ). Δℓ=(π/√gℓ).((2ℓ/100)) =2π√(ℓ/g). (1/100)=(T/100) ∴ (Δ T/T)=(1/100) ∴ 1 %

Q. Time period $T$ of a simple pendulum of length $l$ is given by $T = 2 π \frac{l}{g} .$ If the length is increased by $2%$ , then an approximate change in the time period is

$2%$

$1%$

$\frac{1}{2} %$

None of these

$\frac{d T}{d ℓ} = \frac{2 π}{g} . \frac{1}{2 ℓ}$
$∴ Δ T = \frac{d T}{d ℓ} .Δ ℓ = \frac{π}{g ℓ} . (\frac{2 ℓ}{100})$
$= 2 π \frac{ℓ}{g} . \frac{1}{100} = \frac{T}{100}$
$∴ \frac{Δ T}{T} = \frac{1}{100}$
$∴ 1%$

Q. Time period T of a simple pendulum of length l is given by T=2πgl​​. If the length is increased by 2%, then an approximate change in the time period is

2%

1%

21​%