Accuracy, Precision of Instruments & Errors in Measurement (NCERT) - NEET

∴ The percentage error in density is

= 3% + 3(2%) = 3% + 6% = 9%

Screw gauge has minimum least count of 0.001cm. Hence, it is most precise instrument.

An atomic clock is the most precise time measuring device because atomic oscillations are repeated with a precision of 1s in 10¹³s.

The magnitude of the difference between the true value of the quantity and the individual measurement value is called the absolute error of the measurement. Hence, option (d) is an incorrect statement while all other statements are correct.

(a) Least count of vernier callipers

(∵ 1MSD = 1mm)
(b) Least count of screw gauge

(c) Least count of spherometer

= 0.0001cm
(d) Wavelength of light, λ = 10⁻⁵ cm = 0.00001cm
Clearly the optical instrument is the most precise.

1 MSD = 0.5mm
50VSD = 49MSD
1 VSD = 49/50 MSD
Least Count = 1 MSD - 1 VSD

The mean period of oscillation of the pendulum is

(Rounded off to two decimal places)
The absolute errors in the measurement are
ΔT₁ = 2.62s − 2.63s = −0.01s
ΔT₂ = 2.62s − 2.56s = 0.06s
ΔT₃ = 2.62s − 2.42s = 0.20s
ΔT₄ = 2.62s − 2.71s = −0.09s
ΔT₅ = 2.62s − 2.80s = −0.18s
Mean absolute error is

The relative error in Z is given by

Here, t₁ = 20 °C ± 0.5 °C; t₂ = 50 °C ± 0.5 °C
The temperature difference of two bodies is
t = t₂ - t₁ = 50 °C - 20 °C = 30 °C
The error in temperature difference is given by
Δt = (Δt₁, + Δt₂) = (0.5 °C + 0.5 °C) = 1 °C
∴ The temperature difference is 30 °C ± 1 °C.

The equivalent resistance of series combination is
Rs = R₁ + R₂ = 300Ω + 500Ω = 800Ω
The error in equivalent resistance is given by
ΔR = (ΔR₁ + ΔR₂) = (3 + 4)Ω = 7Ω
Hence, the equivalent resistance along with error is (800 ± 7)Ω.