Using the expression 2 d sin θ = λ , one calculates the values of d by measuring the corresponding angle θ in the range 0 to 90 ° . The wavelength λ is exactly known and the error in θ is constant for all the values of θ . As θ increases from 0 °

The fractional error in d decreases.

The absolute error in d remains constant.

The absolute error in d increases.

The fractional error in d remains constant.

EASY

Earn 100

The permissible error in chaining is 1 in . In an ordinary chain survey the maximum permissible error is 1 in $1000$ .

50% studentsanswered this correctly

Important Questions on Physical World and Measurement

HARD

Physics>Mechanics>Physical World and Measurement>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?

HARD

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

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 s

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

MEDIUM

Physics>Mechanics>Physical World and Measurement>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

EASY

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

A physical quantity z depends on four observables

a, b, c

and

d

, as

z = \frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c} d^{3}} .

The percentage of error in the measurement of

a, b, c

and

d

are

2 %, 1.5 %, 4 %

and

2.5 %

respectively. The percentage of error in

z

is :

EASY

Physics>Mechanics>Physical World and Measurement>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>Physical World and Measurement>Errors in Measurement

A simple pendulum is being used to determine the value of gravitational acceleration

g

at a certain place. The length of the pendulum is

25.0 c m

and a stopwatch with

1 s

resolution measures the time taken for

40

oscillations to be

50 s

. The accuracy in

g

is:

EASY

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

In an experiment, the percentage of error occurred in the measurement of physical quantities

A, B, C

and

D

are 1%, 2%, 3% and 4%, respectively. Then the maximum percentage of error in the measurement

X

, where

X = \frac{A^{2} B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^{3}}

will be

EASY

Physics>Mechanics>Physical World and Measurement>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:

EASY

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be :

MEDIUM

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are

1.5 %

and

1 %

, respectively, the maximum error in determining the density is:

MEDIUM

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is

(\frac{x}{100}) % .

If the relative errors in measuring the mass and the diameter are

6.0 %

and

1.5 %

respectively, the value of

x

-

MEDIUM

Physics>Mechanics>Physical World and Measurement>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>Physical World and Measurement>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>Physical World and Measurement>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:

MEDIUM

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are $0.3 %$ and $0.2 %$ respectively, the maximum error in the estimation of the density of the cube is approximately:

EASY

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

A body accelerates from rest with a uniform acceleration

a

for a time

t .

The uncertainty in '

a

' is

8 %

and the uncertainty in '

t

' is

4 % .

The uncertainty in the speed is

EASY

Physics>Mechanics>Physical World and Measurement>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

MEDIUM

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

A student measures the time period of

100

oscillations of a simple pendulum four times. The data set is

90 s

91 s

95 s

and

92 s

. If the minimum division in the measuring clock is

1 s

, then the reported mean time should be:

MEDIUM

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

Using the expression

2 d \sin θ = λ

, one calculates the values of

d

by measuring the corresponding angle

θ

in the range

0

90 °

. The wavelength

λ

is exactly known and the error in

θ

is constant for all the values of

θ

. As

θ

increases from

0 °

HARD

Physics>Mechanics>Physical World and Measurement>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 ?

The permissible error in chaining is 1 in . In an ordinary chain survey the maximum permissible error is 1 in 1000.

Important Questions on Physical World and Measurement

Learn and Prepare for any exam you want !

The permissible error in chaining is 1 in . In an ordinary chain survey the maximum permissible error is 1 in $1000$ .