if the unit of force work kilonewton, that of time millisecond and that of power kilowatt, what would be the unit of mass and length ?
Answers
Hello Dear.
Here is the answer---
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Given---
Unit of Force = k N
Unit of time = millisecond.
Unit of Power = k W
For the Unit of the Length,
Using the Relation,
Power = Force × Velocity
⇒ Unit of Power = Unit of Force × Unit of Velocity
⇒ 1 k W = 1 k N × Unit of Velocity
⇒ Unit of Velocity = 1kW/1kN
= W/N
=
[Since, 1 W = N/ms]
= 1 m/s.
Now, Using the Formula,
Speed = Distance/Time
Unit of Speed = Unit of Distance/Unit of Time
1 m/s = Unit of Distance/1 millisecond
Unit of Distance = 1 m/s × 1 milliseconds
= 1 m/s × 10⁻³ seconds.
= 1 × 10⁻³ m
= 1 millimeter
We know the unit of length is same as the unit of Distance, thus the unit of length will be 1 millimeter.
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For the unit of Mass,
Using the Formula,
a =
⇒
=
= 10³ m/s²
=1 km/s²
⇒ Unit of acceleration = km/s²
Using the Formula,
Force = Mass × Acceleration
⇒ Unit of Force = Unit of Mass × Unit of Acceleration
⇒ Unit of Mass = Unit of Force/Unit of Acceleration
⇒
⇒
⇒ Unit of Mass = kg.
Thus, the unit of mass will be kg.
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Hope it helps.
Have a Nice day.