Given that, Force = α Density + β 3 . Then the dimensions of α and β are, respectively,

[ M 2 L − 2 T − 2 ] , [ M 1 3 L - 1 ]

[ M L − 2 T − 2 ] , [ M L − 1 3 ]

[ M 2 L 4 T − 2 ] , [ M 1 3 L − 1 ]

[ M 2 L − 2 T − 2 ] , [ M L - 3 ]

Let us consider a system of units in which mass and angular momentum are dimensionless. If the length has a dimension of L , which of the following statement (s) is/are correct?

The dimension of energy is L - 2 .

The dimension of power is L - 5 .

MEDIUM

Physics

IMPORTANT

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The physical quantities not having same dimensions are,

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Important Questions on Physical World and Measurement

HARD

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 4

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

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 5

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

HARD

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 6

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,

HARD

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 7

The potential energy of a particle varies with the distance

x

from a fixed point as,

U = \frac{A \sqrt{x}}{x + B^{2}}

, where,

A

and

B

are constants. Then, the dimension of

A B^{2}

is,

HARD

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 8

Given that, $Force = \frac{α}{Density + β^{3}}$ . Then the dimensions of $α$ and $β$ are, respectively,

HARD

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 9

If velocity

v

, acceleration

A

and force

F

are chosen as fundamental quantities, then, the dimensional formula of angular momentum, in terms of

v

A

and

F

would be

HARD

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 10

If velocity, force and time are taken as the fundamental quantities, then using dimensional analysis choose the correct dimensional formula for mass among the following.

[

K

is a dimensionless constant

]

HARD

Physics

IMPORTANT

Physics Crash Course JEE Advanced>Chapter 1 - Physical World and Measurement>Exercise 1>Q 11

A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation

(T)

of the liquid drop depends on radius

(r)

of the drop, density

(ρ)

and surface tension

(S)

of the liquid. Which among the following will be a possible expression for

T

(where,

k

is a dimensionless constant )?

The physical quantities not having same dimensions are,

Important Questions on Physical World and Measurement

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