A student performs an experiment for determination of The error in length is and in time is and is the number of times the reading is taken. The measurement of is most accurate for [2006]

Question

A student performs an experiment for determination of $(g = \frac{4 π^{2} ℓ}{T^{2}} .)$ The error in length $ℓ$ is $Δ ℓ$ and in time $T$ is $Δ T$ and $n$ is the number of times the reading is taken. The measurement of $g$ is most accurate for [2006]

Smart Achievers · Accepted Answer

(4)

$Relative error in g, \frac{Δ g}{g} = \frac{Δ ℓ}{ℓ} + 2 \frac{Δ T}{T}$

$Δ ℓ and Δ T are least and number of readings taken are maximum in option (d),$

$∴ the measurement of g is most accurate.$

Solution

Q.
A student performs an experiment for determination of $(g = \frac{4 π^{2} ℓ}{T^{2}} .)$ The error in length $ℓ$ is $Δ ℓ$ and in time $T$ is $Δ T$ and $n$ is the number of times the reading is taken. The measurement of $g$ is most accurate for [2006]

1 $Δ ℓ = 5 mm, Δ T = 0.2 sec, n = 10$

2 $Δ ℓ = 5 mm, Δ T = 0.2 sec, n = 20$

3 $Δ ℓ = 5 mm, Δ T = 0.1 sec, n = 10$

4 $Δ ℓ = 1 mm, Δ T = 0.1 sec, n = 50$

Ans.
(4)

$Relative error in g, \frac{Δ g}{g} = \frac{Δ ℓ}{ℓ} + 2 \frac{Δ T}{T}$

$Δ ℓ and Δ T are least and number of readings taken are maximum in option (d),$

$∴ the measurement of g is most accurate.$

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Solution

Q. A student performs an experiment for determination of (g=4π2ℓT2.) The error in length ℓ is Δℓ and in time T is ΔT and n is the number of times the reading is taken. The measurement of g is most accurate for [2006]

1 Δℓ=5 mm, ΔT=0.2 sec, n=10

2 Δℓ=5 mm, ΔT=0.2 sec, n=20

3 Δℓ=5 mm, ΔT=0.1 sec, n=10

4 Δℓ=1 mm, ΔT=0.1 sec, n=50

Ans. (4) Relative error in g, Δgg=Δℓℓ+2ΔTT Δℓ and ΔT are least and number of readings taken are maximum in option (d), ∴ the measurement of g is most accurate.