EASY

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A metal wire has mass ( $0.4 \pm 0.002$ ) $g$ , radius ( $0.3 \pm 0.001$ ) $mm$ and length ( $5 \pm 0.02$ ) $cm$ . The maximum possible percentage error in the measurement of density will nearly be:

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Important Questions on Units and Measurements

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

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 \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 statements (s) is (are) true?

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

In the density measurement of a cube, the mass and edge length are measured as

(10.00 \pm 0.10) k g

and

(0.10 \pm 0.01) m,

respectively. The error in the measurement of density is:

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A cylindrical wire has a mass

(0.3 \pm 0.003) g

, radius

(0.5 \pm 0.005) mm

and length

(6 \pm 0.06) cm

. The maximum percentage error in the measurement of its density is

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The period of oscillation of a simple pendulum is

T = 2 π \sqrt{\frac{L}{g}} .

Measured value of

L

1.0 m

from meter scale having a minimum division of

1 mm

and time of one complete oscillation is

1.95 s

measured from stopwatch of

0.01 s

resolution. The percentage error in the determination of

' g'

will be:

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

In an experiment, the mass of an object is measured by applying a known force on it, and then measuring its acceleration. If in the experiment, the measured values of applied force and the measured acceleration are

F = (10.0 \pm 0.2) N

and

a = (1.00 \pm 0.01) m s^{- 2},

respectively, the mass of the object is

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

If the error in the measurement of radius of a sphere is

1 %

, the error in the measurement of volume will be

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

Time intervals measured by a clock give the following readings: $1.25 s, 1.24 s, 1.27 s, 1.21 s$ and $1.28 s$ . What is the percentage relative error of the observations?

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

Let

x = [\frac{a^{2} b^{2}}{c}]

be the physical quantity. If the percentage error in the measurement of physical quantities

a

b

and

c

2

3

and

4

percent respectively then percentage error in the measurement of

x

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The length and width of a rectangular room are measured to be

(3 .95 \pm 0 .05) m

and

(3 .05 \pm 0 .05) m

, respectively, the area of the floor is

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A physical quantity $P$ is described by the relation $P = a^{\frac{1}{2}} b^{2} c^{3} d^{- 4}$ . If the relative errors in the measurement of $a$ , $b$ , $c$ and $d$ respectively, are $2 %$ , $1 %$ , $3 %$ and $5 %$ . Then the relative error in $P$ will be:

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The time period of a simple pendulum is given by

T = 2 π \sqrt{\frac{l}{g}} .

The measured value of the length of the pendulum is

10 cm

known to a

1 mm

accuracy. The time for

200

oscillations of the pendulum is found to be

100

second using a clock of

1 s

resolution. The percentage accuracy in the determination of

g

using this pendulum is

x .

The value of

x

to the nearest integer is:-

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The percentage errors in quantities

P

Q

R

and

S

are

0.5 %

1 %

3 %

and

1.5 %

respectively in the measurement of a physical quantity

A= \frac{P^{3} Q^{2}}{\sqrt{R} S}

. The maximum percentage error in the value of

A

will be:

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

In the experiment of Ohm's law, a potential difference of

5.0 V

is applied across the end of a conductor of length

10.0 cm

and diameter of

5.00 mm .

The measured current in the conductor is

2.00 A .

The maximum permissible percentage error in the resistivity of the conductor is :-

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The resistance

R = \frac{V}{I}

where,

V = (100 \pm 5) V

and

I = (10 \pm 0.2) A .

The percentage error in

R

is:

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

Student No.	Length of pendulum $(cm)$	Number of oscillations $(n)$	Total time for $n$ oscillations	Time period $(s)$
$1 .$	$64.0$	$8$	$128.0$	$16.0$
$2 .$	$64.0$	$4$	$64.0$	$16.0$
$3 .$	$20.0$	$4$	$36.0$	$9.0$

(Least count of length $= 0.1 m$ , least count for time $= 0.1 s$ )

If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $g$ for students $1, 2$ and $3$ , respectively, then the minimum percentage error is obtained by student no $.$

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

Consider a physical quantity,

Z

expressed as

Z = \frac{A B^{\frac{1}{2}}}{C^{2}} .

If the relative error in the magnitudes of

A, B

and

C

1 %

then the relative error in

Z

will be,

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The acceleration due to gravity is found up to an accuracy of

4 %

on a planet. The energy supplied to a simple pendulum of known mass

m

to undertake oscillations of time period

T

is being estimated. If time period is measured to an accuracy of

3 %

, the accuracy to which

E

is known as ________

%

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

In a simple pendulum experiment for determination of acceleration due to gravity

(g)

, time taken for

20

oscillations is measures by using a watch of

1

second least count. The mean value of time taken comes out to be

30 s

. The length of the pendulum is measured by using a meter scale of least count

1 m m

and the value obtained is

55.0 c m

. The percentage error in the determination of

g

is close to

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

If one takes into account the finite mass of the proton, the correction to the binding energy of the hydrogen atom is approximately (mass of proton

= 1 .60 \times 10^{- 27} kg,

mass of an electron

= 9 .10 \times 10^{- 31} kg

)

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

The current voltage relation of diode is given by I = (e¹⁰⁰⁰^V/T - 1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring

\pm 0.01 V

while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

A metal wire has mass (0.4±0.002) g, radius (0.3±0.001) mm and length (5±0.02) cm. The maximum possible percentage error in the measurement of density will nearly be:

Important Questions on Units and Measurements

Learn and Prepare for any exam you want !

A metal wire has mass ( $0.4 \pm 0.002$ ) $g$ , radius ( $0.3 \pm 0.001$ ) $mm$ and length ( $5 \pm 0.02$ ) $cm$ . The maximum possible percentage error in the measurement of density will nearly be: