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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In a meter bridge circuit, the known resistance used in resistance box is $100 Ω$ (without any error and the unknown resistor is put in right arm). The null point is found to be $40 cm$ from the left end. If $mm$ scale is used in the meter bridge then the resistance of the unknown resistor is:

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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 - 1>Q 18

In the formula

X = 3 Y Z^{2}

, the quantities

X

and

Z

have the dimensions of capacitance and magnetic induction, respectively. The dimensions of

Y

in the MKS system are,

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Alpha Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise - 1>Q 19

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

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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 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?

In a meter bridge circuit, the known resistance used in resistance box is 100 Ω (without any error and the unknown resistor is put in right arm). The null point is found to be 40 cm from the left end. If mm scale is used in the meter bridge then the resistance of the unknown resistor is:

Important Questions on Physical World and Measurement

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In a meter bridge circuit, the known resistance used in resistance box is $100 Ω$ (without any error and the unknown resistor is put in right arm). The null point is found to be $40 cm$ from the left end. If $mm$ scale is used in the meter bridge then the resistance of the unknown resistor is: