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If the speed of light $c$ , acceleration due to gravity $g$ and pressure $p$ are taken as the fundamental quantities, then the dimension of the universal gravitational constant 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 6

If the time period

T

of vibration, of a liquid drop, depends on surface tension

S

, the radius

r

of the drop and the density

ρ

of the liquid, then the expression of

T

is (Take

K

as dimensional constant)

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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 7

If pressure $P$ velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is

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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 8

If energy

E

, velocity

V

and force

F

are taken as fundamental quantities, then what are the dimensions of mass?

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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 9

A physical quantity

x

depends on quantities

y

and

z

as follows,

x = A y + B \tan (C z)

where

A

B

and

C

are constants. Which of the following do not have the same dimensions?

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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 10

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

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

MEDIUM

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

If the speed of light c, acceleration due to gravity g and pressure p are taken as the fundamental quantities, then the dimension of the universal gravitational constant is

Important Questions on Unit Dimension and Measurement

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If the speed of light $c$ , acceleration due to gravity $g$ and pressure $p$ are taken as the fundamental quantities, then the dimension of the universal gravitational constant is