If the speed v of a particle, of mass m , as a function of time t , is given by v = ω A sin k m t , where A has dimension of length. Choose the correct option.

The angle of the trigonometric function must be a dimensionless quantity.

Dimensional formula of ω is LT - 1 .

Dimensional formula of k is MLT - 2 .

Dimensional formula of k m is T .

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JEE Main

IMPORTANT

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If the velocity of light $c$ , gravitational constant $G$ and Planck’s constant $h$ are chosen as fundamental units, then the dimensions of mass, in the new system, is

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Important Questions on Unit Dimension and Measurement

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 11

If force

(F)

, length

(L)

and time

(T)

are assumed to be fundamental units, then the dimensional formula of the mass will be

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 12

Position of a body, with acceleration

a

, is given by

x = K a^{m} t^{n}

where,

t

is time and

K

is a dimensionless constant. Find the values of

m

and

n

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 13

In a system of units, if force

F

, acceleration

A

and time

T

are taken as fundamental units, then the dimensional formula of energy is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 14

The density of a liquid in the CGS system is

0.625 g {cm}^{- 3}

. What is its magnitude in the SI system?

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 15

If the speed

v

of a particle, of mass

m

, as a function of time

t

, is given by

v = ω A \sin [(\sqrt{\frac{k}{m}}) t]

, where

A

has dimension of length. Choose the correct option.

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 1

Time for

20

oscillations, of a pendulum, is measured as

t_{1} = 39 .6 s

t_{2} = 39 .9 s

and

t_{3} = 39.5 s

. What is the precision in the measurements? What is the accuracy of the measurement?

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 2

A physical quantity

X

is related to four measurable quantities,

a

b

c

and

d

X = a^{2} b^{3} c^{5 ⁄ 2} d^{- 2}

. The percentage error in the measurement of

a

b

c

and

d

are

1 %

2 %

3 %

and

4 %

, respectively. What is the percentage error in quantity

X

? If the value of

X

, calculated on the basis of the above relation, is

2.763

, to what value should you round off the result?

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I JEE Main & Advanced>Chapter 1 - Unit Dimension and Measurement>DPP>Q 3

What is the number of significant figures in $0.310 \times 10^{3}$ ?

If the velocity of light c, gravitational constant G and Planck’s constant h are chosen as fundamental units, then the dimensions of mass, in the new system, is

Important Questions on Unit Dimension and Measurement

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If the velocity of light $c$ , gravitational constant $G$ and Planck’s constant $h$ are chosen as fundamental units, then the dimensions of mass, in the new system, is