Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-4>Q 3

EASY

JEE Main/Advance

IMPORTANT

Earn 100

A particle of mass $m$ is in a uni-directional potential field where the potential energy of a particle depends on the $x$ - coordinate given by $ϕ_{x} = ϕ_{0} (1 - cosax)$ and ' $ϕ_{0}$ ' and ' $a$ ' constants. Find the physical dimensions of ' $a$ ' and $ϕ_{0}$ .

Important Questions on Physical World and Measurement

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-4>Q 4

In the formula,

p = \frac{n R T}{V - b} e^{\frac{a}{R T V}},

find the dimensions of

a

and

b,

where

p =

pressure,

n =

number of moles,

T =

temperature,

V =

volume and

R =

universal gas constant.

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-4>Q 5

If instead of mass, length and time as fundamental quantities we choose velocity, acceleration and force as fundamental quantities and express their dimensional symbols as

v, a

and

F

respectively. Show that the dimensions of Young's modulus can be expressed as

[{Fa}^{2} v^{- 4}]

.

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-4>Q 6

If energy

(E)

, velocity

(v)

and time

(T)

are fundamental units then the dimension of surface tension is

[{Ev}^{- α} T^{- β}]

. Find

α - β

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-4>Q 7

In a system called the star system we have

1

star kilogram

= 10^{20} kg

.

1

star meter

= 10^{8} m

,

1

star second

= 10^{3}

second. If the value of

1

joule in this system is

10^{- 10 α} star joule

, then find

α

.

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-4>Q 8

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and Earth in terms of the new unit if light takes

8 \min

and

20 s

to cover this distance?