In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?

(A) The error in the measurement of $r$ is 10\%; (B) The error in the measurement of $T$ is $3.57 \%$; (D) The error in the determined value of $g$ is $11 \%$

(C) The error in the measurement of $T$ is 2\%

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Units & Measurement

WhatsApp Email

In an experiment to determine the acceleration due to gravity

g

, the formula used for the time period of a periodic motion is

T = 2 π \frac{7 ( R - r )}{5 g}

. The values of

R

and

r

are measured to be

(60 \pm 1) mm

and

(10 \pm 1) mm

, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?

(A)The error in the measurement of $r$ is 10%✓ Correct
(B)The error in the measurement of $T$ is $3.57%$ ✓ Correct
(C)The error in the measurement of $T$ is 2%
(D)The error in the determined value of $g$ is $11%$ ✓ Correct

Answer: (A), (B), (D)

Solution

Error in

r

\frac{Δ r}{r} = \frac{1}{10} = 10%

✓ (A)

Mean time period:

T_{m e an} = \frac{0.52 + 0.56 + 0.57 + 0.54 + 0.59}{5} = 0.556 \approx 0.56

s

Mean deviation:

Δ T = 0.02

s

Error in T:

\frac{0.02}{0.56} \times 100 = 3.57%

✓ (B)

From

g = \frac{28 π ^{2}}{5} \frac{R - r}{T ^{2}}

\frac{Δ g}{g} = \frac{Δ R + Δ r}{R - r} + 2 \frac{Δ T}{T} = \frac{2}{50} + 2 (0.0357) = 0.04 + 0.0714 \approx 11%

✓ (D)

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · One or more correct options

Practise more: all JEE Advanced PYQs on Units & Measurement →

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Units & Measurement

Solution

More JEE Advanced questions on Units & Measurement