PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 11

HARD

JEE Advanced

IMPORTANT

Earn 100

The velocity, acceleration and force in two systems of units are related as,

$(i) v' = \frac{α^{2}}{β} v$
$(ii) a' = (α β) a$
$(iii) F' = (\frac{1}{α β}) F$
All primed symbols belong to one system and the unprinted ones belong to other system, $α$ and $β$ are dimensionless constants. Which of the following statements is/are true?

50% studentsanswered this correctly

Important Questions on Dimensions and Measurement

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 12

The gas equation for

n

moles of a real gas is,

[P + \frac{a}{V^{2}}] (V - b) = n R T

, where

P

is the pressure,

V

is the volume,

T

is the absolute temperature,

R

is the molar gas constant and

a, b

are arbitrary constants. Which of the following has/have the same dimensions as that of

P V

?

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 13

If

y = a^{3} \sin^{- 1} (\frac{x}{b} - 1)

, where

y

is in metre, then,

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 14

The speed of a particle depends on the time

t

as

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

. Then,

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 15

Pressure

P

of a gas is given in terms of time

t

as

P = A sinbt + B sinct

. Then,

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 16

Consider the equation,

(A + \frac{B}{C^{2}}) (D - x) = y

. Then,

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 17

The error in measurement of radius of a sphere is

1 %

. Then,

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 18

Error in measurement of volume of a sphere is

9 %

, then:

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 1 - Dimensions and Measurement>Exercises>Q 19

P

,

ρ

,

g

and

h

denote pressure, density, acceleration due to gravity and height, respectively. In the case of flow of fluid,

\frac{P}{ρ g} + \frac{v^{2}}{2 g} + h = u_{0}

, where

v

denotes velocity. Mark the correct option(s).