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The time period of small oscillation of surface of liquid drop depends on its surface tension, density of liquid and its mean radius. Find the time period by dimensional analysis. If we measure the mean radius, it has error of 2%, surface tension and density both have an error of 1%. Find the percentage error in measurement of time period.

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Important Questions on Units and Measurements

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 period of oscillation of a simple pendulum is given by

T = 2 π \sqrt{\frac{L}{g}}

, where

L

is the length of the pendulum and

g

is the acceleration due to gravity. The length is measured using a meter scale which has

500

divisions. If the measured value

L

50 cm

, the accuracy in the determination of

g

1.1 %

and the time taken for

100

oscillations is

100

seconds, what should be the possible error in measurement of the clock in one minute (in milliseconds)?

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

MEDIUM

Physics>Mechanics>Units and Measurements>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>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:

MEDIUM

Physics>Mechanics>Units and Measurements>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>Units and Measurements>Errors in Measurement

Two students $P$ and $Q$ perform an experiment to verify Ohm's law for a conductor with resistance $R$ . They use a current source and a voltmeter with the least counts of $0.1 mA$ and $0.1 mV$ , respectively. The plots of the variation of voltage drop $V$ across $R$ with current $I$ for both are shown below.

Question Image

The statement which is most likely to be correct?

EASY

Physics>Mechanics>Units and Measurements>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:

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

)

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

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

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

A student measured the diameter of a small steel ball using a screw gauge of least count

0.001 cm

. The main scale reading is

5 mm

and

25^{t h}

division of circular scale coincides with reference line. If screw gauge has a zero error of

- 0.004 cm

, the correct diameter of the ball is

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

EASY

Physics>Mechanics>Units and Measurements>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 :

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

Using screw gauge of pitch

0.1 cm

and

50

divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as,

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The power in an electrical circuit for a current of

5 \pm 0.4 A

and voltage

10 \pm 0.2 V

is measured at

10 %

error. To measure the power at

5 %

error the current should be measured at an error of

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The length of an object is measured using a vernier system whose main scale is

30 cm

long with

600

divisions. If

19

divisions of the main scale coincide with

20

divisions of the vernier scale, then its least count is

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it ?

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The relative error in the determination of the surface area of a sphere is

α

. The relative error in the determination of its volume is

Important Questions on Units and Measurements

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