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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JEE Advanced

IMPORTANT

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There are two Vernier calipers both of which have $1 cm$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $(C_{1})$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $(C_{2})$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $cm$ ) by calipers $C_{1}$ and $C_{2}$ respectively, are

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Important Questions on Dimensions and Measurement

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 7

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

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 1

A student uses a simple pendulum of exactly

1 m

length to determine

g

, the acceleration due to gravity. He uses a stop watch with the least count of

1 s

for this and records

40 s

for

20

oscillations. For this observation, which of the following statement(s) is(are) true?

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 2

Planck's constant

h

, speed of light

c

and gravitational constant

G

are used to form a unit of length

L

and a unit of mass

M

. Then the correct options(s) is (are)

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 3

In terms of potential difference

V

, electric current

I

, permittivity

ε_{0}

, permeability

μ_{0}

and speed of light

c

, the dimensionally correct equations(s) is (are)

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 4

A length scale

(l)

depends on the permittivity

(ε)

of a dielectric material, Boltzmann constant

k_{B}

, the absolute temperature

T

, the number per unit volume

(n)

of certain charged particles, and the charge

(q)

carried by each of the particles. Which of the following expressions(s) for

l

is(are) dimensionally correct?

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 5

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?

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 1

To find the distance

d

over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density

ρ

of the fog, intensity

(power / area)

S

of the light from the signal and its frequency

f

. The engineer finds that

d

is proportional to

S^{\frac{1}{n}}

. The values of

n

is,

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Archives>Q 2

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

Important Questions on Dimensions and Measurement

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