Question

3. Find the units of mass and length if the unit of force is Mega Newton, unit
of power is watt and unit of time is 1 microsecond.​

Answer 1

Answer:

F]=[MLT

−2

] and [P]=[ML

2

T

−1

]⇒

F

2

P

=

M

T

3

⇒[M]=

P

F

2

T

3

Unit of mass =

(10

3

)

(10

3

)

2

(10

−3

)

3

= 1kg

Answer 2

The unit of length is 10⁻³ meter and the unit of mass is 1 kg

GIVEN

Unit of force = Mega Newton.

Unit of Power = Watt

Unit of Time = 1 microsecond.

TO FIND

Units of Mass and length.

SOLUTION

We can simply solve the above problem as follows-

we know that,

1 kiloWatt = 10³Watt

1 Mega Newton = 10³N

1 microsecond = 10⁻³ sec

Power = Energy/Time. (Formula 1 )

And,

Energy or work done = Force × displacement.

Putting it in Formula 1, we get-

Power = Force × displacement/Time.

Let displacement be, l

Putting all the values in the above formula we get

${10}^{3} = \frac{ {10}^{3} \times l}{ {10}^{ - 3} }$

$l = {10}^{ - 3} meter$

Now, To find the units of force, we will apply the the following formula

Force = Mass × Acceleration

Where,

Acceleration = Change of speed /time taken

F = M × v/t

So,

F = M × d/t × t

We can distance, d = l

Now, Putting all the values in the above equation we get,

${10}^{3} = \frac{m \times {10}^{ - 3} }{ { ( {10}^{ - 3} ) }^{2} }$

Solving for m

m = 1 kg

Hence, The unit of length is 10⁻³ meter and the unit of mass is 1 kg

#spj2

For more such questions -

https://brainly.in/question/12852033?utm_source=android&utm_medium=share&utm_campaign=question

https://brainly.in/question/2604249?utm_source=android&utm_medium=share&utm_campaign=question