Physics

If we choose velocity V, acceleration A and force F as the fundamental quantities, then the angular momentum in terms of V,A and F would be :


ANSWER

$$[FV^{3}A^{-2}]$$


SOLUTION
 We know that ,
$$\left[F\right]= \left[{MLT}^{-2}\right] , \left[V\right] \left[{M}^{0}{LT}^{-1}\right],$$
$$\left[A\right]= \left[{LT}^{-2}\right]$$ and $$\left[\vec L \right] =\left[M{L}^{2}{T}^{-1}\right] $$

Where$$ \vec L$$is the angular momentum 
let $$\quad \quad \quad \left[ \vec { L }  \right] ={ \left[ F \right]  }^{ a }{ \left[ V \right]  }^{ b }{ \left[ A \right]  }^{ c }$$  

$$\Rightarrow \left[M{L}^{2}{T}^{-1}\right]= {\left[{MLT}^{-2}\right]}^{a} {\left[{LT}^{-1}\right]}^{b} {\left[{LT}^{-2}\right]}^{c}$$

$$\Rightarrow \left[M{L}^{2}{T}^{-1}\right]= \left[{M}^{\left(a\right)} {L}^{\left(a+b+c\right)} {T}^{\left(-2a-b-2c\right)}\right]$$

By analysing , we get
$$a=1$$
$$a+b+c=2$$
$$2a+b+2c=1$$

By solving these equations , we get 
$$a=1, \quad b=3 $$ $$c=-2$$

So , $$\left[‘L’\right]= \left[F{V}^{3}{A}^{-2}\right]$$
Option $$B$$ is correct .

View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Single Correct Medium Published on 18th 08, 2020
Next Question
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 204
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
The dimension of electrical conductivity is _________.
  • A. $$M^{-2}L^{-4}T^3A^2$$.
  • B. $$M^{-1}L^{-3}T^3A^2$$.
  • C. $$M^{-1}L^{-3}T^4A^2$$.
  • D. $$M^{-2}L^{-3}T^6A^2$$.

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q2 Subjective Medium
In an experiment, refractive index of glass was observed to be 1.45, 1.56, 1.54, 1.44, 1.54, and 1.53 Calculate
 Mean absolute error

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q3 Single Correct Medium
Frictional force can't be measured in
  • A. kg wt
  • B. Newton
  • C. Dyne
  • D. $$\displaystyle kg{ ms }^{ -1 }$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q4 One Word Medium
The volume of a gas is ______  time the initial volume when the pressure is reduced to half and the absolute temperature is doubled.

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q5 Single Correct Medium
How many order of magnitude are there in one million?
  • A. 5
  • B. 4
  • C. 6
  • D. None of above

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer