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A gas bubble, formed from an explosion under water, oscillates with a period proportional to $P^{a} d^{b} E^{c}$ , where, $P$ is the static pressure, $d$ is the density of water and $E$ is the energy of explosion. Then, $a, b and c$ are, respectively,

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Important Questions on Units and Measurement

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 39

The frequency

f

of vibrations of a mass

m

, suspended from a spring of spring constant

k

, is given by

f = C m^{x} k^{y},

where,

C

is a dimensionless constant. The values of

x

and

y

are, respectively,

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Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 40

In a certain system, the units of length, mass and time are chosen to be

1 cm, 100 g

and

10 s

, respectively. The unit of kinetic energy will be,

HARD

NEET

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Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 41

The dimension of

\frac{a}{b}

in the relation,

P = \frac{a - t^{2}}{b x}

, where,

P

is the pressure,

x

is the distance and

t

is the time, is:

HARD

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 42

The speed of light in vacuum is given by

3 \times 10^{8} m s^{- 1}

in the MKS system. If in a new system, the unit of length and time is increased by a factor of

2

and

4

, respectively, the numerical value of speed of light in this new system will be

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Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 43

The force on a particle in one-dimensional motion is given by,

F = A v + B t + \frac{C x}{A t + D}

, where,

F

is force,

v

is speed,

t

is time,

x

is position and

A, B, C

and

D

are constants. The dimensions of

C

will be,

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Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 44

Given that,

v

is speed,

r

is radius and

g

is the acceleration due to gravity. Which of the following is dimensionless?

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Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 45

The strong nuclear force inside a nucleus is given by,

F = \frac{C e^{- kr}}{r^{2}}

, where,

r

is the position. The dimensions of

C

and

k

are, respectively,

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Chapterwise/Topicwise Daily Practice Problems (DPP) Mechanics I NEET>Chapter 2 - Units and Measurement>TOPICWISE QUESTIONS>Q 46

Suppose refractive index

μ

is given as

μ = A + \frac{B}{λ^{2}}

, where

A

and

B

are constants and

λ

is the wavelength, then dimensions of

B

are same as that of

A gas bubble, formed from an explosion under water, oscillates with a period proportional to PadbEc, where, P is the static pressure, d is the density of water and E is the energy of explosion. Then, a, b and c are, respectively,

Important Questions on Units and Measurement

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A gas bubble, formed from an explosion under water, oscillates with a period proportional to $P^{a} d^{b} E^{c}$ , where, $P$ is the static pressure, $d$ is the density of water and $E$ is the energy of explosion. Then, $a, b and c$ are, respectively,