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 force $(F)$ , length $(L)$ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be

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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 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?

EASY

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 $0.310 \times 10^{3}$ ?

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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 4

The number of significant figures in

0.06900

If force (F), length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be

Important Questions on Unit Dimension and Measurement

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If force $(F)$ , length $(L)$ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be