Question

if the unit of force were kilonewton,that of time millisecond and that of power is kilowatt what would be the unit of mass and length

Answer 1

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
                              = $\frac{N/ms}{N}$ 
                            [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,

 $Acceleration = \frac{Final Velocity - Initial Velocity}{time}$
                 a = $\frac{v - u}{t}$
        ⇒ $Unit of a = \frac{ unit of (v - u)}{unit of t}$
                                 = $\frac{1 m/s}{1 milliseconds}$
                                 = 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
   ⇒  $Unit of Mass = \frac{k N}{k m/s^{2} }$
  ⇒ $Unit of mass = \frac{ kg m/s^{2} }{m/s^{2} }$
  ⇒ Unit of Mass = kg.

Thus, the unit of mass will be kg.


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Hope it helps.


Have a Nice day.