Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 4

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If the unit of length be doubled then the numerical value of the universal gravitation constant $G$ will become (with respect to present value)

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Important Questions on Physical World and Measurement

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 5

The dimensionless quantity

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 6

Bernoulli’s equation is given by

p + \frac{1}{2} {ρv}^{2} + hρg = k

Where

p =

pressure,

ρ =

density,

v =

speed,

h =

height of the liquid column,

g =

acceleration due to gravity and

k

is constant. The dimensional formula for

k

is same as that for :

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 7

When a wave travels in a medium, the displacement of a particle located at distance

x

at time

t

is given by

y = a \sin (b t - c x)

where

a, b

and

c

are constants of the wave. The dimensions of

\frac{b}{c}

are the same as that of

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 8

The Van der Waal's equation of a gas is

(P + \frac{a T^{2}}{V}) V^{c} = (R T + b)

, where

a, b, c

and

R

are constants. If the isotherm is represented by

P = A V^{m} - B V^{n}

, where

A

and

B

depends on temperature, then

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 9

The quantities,

A

and

B

, are related by the relation

m = \frac{A}{B}

, where

m

is the linear mass density and

A

is the force. The dimensions of

B

are of

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 10

A physical quantity

x

can be dimensionally represented in terms of

M, L

and

T

that is

x = M^{a} L^{b} T^{c}

. The quantity time

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 11

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 this new system is

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Beta Question Bank for Engineering: Physics>Chapter 3 - Physical World and Measurement>Exercise-2>Q 12

Calorie is a unit of heat or energy whose value is

4.2 J

, where

J = 1 {kgm}^{2} s^{- 2}

. If one uses a unit system in which units of mass, length and time are taken as

α kg, β

metre and

γ

second respectively, then the value of calorie in this system will be-