Dimensions of Energy in Terms of Fundamental Quantities F, A and T Are

By Team Aakash Byju's | 16th November 2022

A. [F]  [A]  [T]

C. [F]  [A]  [T]

B. [F]  [A]  [T]

D. [F]  [A]  [T]

2

2

2

2

2

2

2

Your options are

Arrow

The correct answer is  C. [F][A][T] .

Detailed Explanation

2

We know that the dimensions for Energy are

M  L  T

1

2

2

The dimensions for Force, Acceleration and Time are given below.

F = M  L  T   ,

A =L  T  and T = T

1

1

2

1

1

2

So, when energy is written in terms of force F, acceleration A and time T can be written as

M  L  T   =

(M  L  T  )   (L  T   )   (T  )

1

1

1

1

1

2

2

2

2

x

y

z

Solve the expression using the rules of exponents and equate the powers

=>1 = x, 2 = x+y

and

2 = 2x-2y+z

Since, x = 1 and x+y=2, we get  y = 1.

2 = 2x-2y+z = 2

=> 2-2 = z

then, z = 2.

And, When

Using the values of x, y & z in Step 5, we get,

M  L  T  =

(M  L  T  )   (L  T   )  (T  )

1

1

1

1

1

2

2

2

2

1

1

2

=> E  = F  A  T

2

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