Question

SI unit of 1500g and 5km without changing there volumes​

Answer 1

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A new system of units is proposed in which unit of mass is α kg, unit of length is β m and unit of time is γ s. What will be value of 5 J in this new system?

A

5αβ

2

γ

−2

B

5α

−1

β

2

γ

2

C

5α

−2

β

−1

γ

−2

D

5α

−1

β

−

2γ

2

HARD

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ANSWER

Joule is a unit of energy.

SI New system

n

1

=5 n

2

=?

M

1

=1kg M

2

=αkg

L

1

=1m L

2

=βm

T

1

=1s T

2

=γs

Dimensional formula of energy is [ML

2

T

−2

]. Comparing with [M

a

L

b

T

c

], we get

a = 1, b = 2,c = -2

As n

2

=n

1

(

M

2

M

1

)

a

(

L

2

L

1

)

b

(

T

2

T

1

)

c

=5(

αkg

1kg

)

1

(

βm

1m

)

2

(

γs

1s

)

−2

=

αβ

2

5γ

2

=5α

−1

β

−2

γ

2