In an experiment to determine the acceleration due to gravity g , the formula used for the time period of a period of a periodic motion is, T = 2 π 7 R - r 5 g . The values of R and r are measured to be 60 ± 1 mm and 10 ± 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?

The error in the determined value of g is 11 % .

The error in the measurement of T is 2 % .

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The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are :

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Important Questions on Physical World and Measurement

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 2>Q 1

Let $[ε_{o}]$ denote the dimensional formula of the permittivity of the vacuum and $[μ_{o}]$ that of the permeability of the vacuum. If

$M =$ mass, $L =$ length, $T =$ time and $I =$ electric current.

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 3>Q 1

A student performs an experiment for determination of

g = \frac{4 π^{2} l}{T^{2}}, l \approx 1 m

and he commits an error of

∆ l

. For

T

, he takes the time of

n

oscillations with the stopwatch of the least count

∆ T

and he commits a human error of

0.1 s

. For which of the following data, the measurement of

g

will be most accurate?

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 3>Q 2

A student performs an experiment to determine Young's modulus of a wire, exactly

2 m

long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be

0.8 mm

with an uncertainty of

\pm 0.05 m m

at a load of exactly

1.0 kg

. The student also measures the diameter of the wire to be

0.4 mm

with an uncertainty of

\pm 0.01 m m

. Take

g = 9.8 m s^{- 2}

(exact). The Young's modulus obtained from the reading is

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 3>Q 3

Student $I, II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $= 0.1 cm$
Least count for time $= 0.1 s$

Student	Length of the pendulum $(cm)$	Number of oscillations $(n)$	Total time for $(n)$ oscillations $(s)$	Time period $(s)$
$I$	64.0	8	128.0	16.0
$II$	64.0	4	64.0	16.0
$III$	20.0	4	36.0	9.0

If $E_{I}, E_{II}$ and $E_{III}$ are the percentage errors in $g$ , i.e., $(\frac{∆ g}{g} \times 100)$ for students $I, II$ and $III$ , respectively,

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 3>Q 4

In the determination of Young's modulus

(\begin{matrix} Y = & \frac{4 M L g}{π l d^{2}} \end{matrix})

by Searle's method, a wire of length

L = 2 m

and diameter

d = 0.5 mm

is used. For a load

M = 2.5 kg

, an extension

l = 0.25 mm

in the length of the wire observed. Quantities d and l are measured using screw gauge and a micrometer, respectively. They have the same pitch of

0.5 mm

. The number of divisions on their circular scale is

100

. The contributions to the maximum probable error of the Y measurement

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 3>Q 6

The energy of a system as a function of time

t

is given as

E (t) = A^{2} \exp (- α t)

, where

α = 0.2 s^{- 1}

. The measurement of

A

has an error of

1.25 %

. If the error in the measurement of time is

1.50 %,

the percentage error in the value of

E (t)

t = 5 s

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 3>Q 7

In an experiment to determine the acceleration due to gravity

g

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

T = 2 π \sqrt{\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?

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 3>Q 8

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is

δ T = 0.01

second and he measures the depth of the well to be

L = 20 meters

. Take the acceleration due to gravity

g = 10 {m s}^{- 2}

and the velocity of sound is

300 {m s}^{- 1}

. Then the fractional error in the measurement

\frac{δ L}{L}

is closest to

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are :

Important Questions on Physical World and Measurement

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