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Taking force (F), velocity (V) and time (T) to be the fundamental quantity, find the dimension of the momentum.

Taking force (F), velocity (V) and time (T) to be the fundamental quantity, find the dimension of the momentum. Correct Answer [F<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em; font-size:10.5px;">1</span> V<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em; font-size:10.5px;">0</span> T<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em; font-size:10.5px;">1</span>]

CONCEPT:

Dimensions:

  • Dimensions of a physical quantity are the powers to which the fundamental units are raised to obtain one unit of that quantity.

​
CALCULATION:

  • We know that the dimension of the force is given as,


⇒  =      -----(1)

  • We know that the dimension of the velocity is given as,


⇒  =      -----(2)

  • We know that the dimension of the time is given as,


⇒  =      -----(3)

  • We know that the dimension of the momentum is given as,


⇒  =      -----(4)

  • If force (F), velocity (V), and time (T) to be the fundamental quantity, then the dimension of the momentum is given as,


⇒  =      -----(5)

By equation 1, equation 2, equation 3, equation 4 and equation 5,

⇒ x × y × z = 

⇒  =      -----(6)

By equation 6,

⇒ x = 1     -----(7)

⇒ x + y = 1     -----(8)

⇒ -2x + z = -1     -----(9)

By equation 7, equation 8, and equation 9,

⇒ x = 1

⇒ y = 0

⇒ z = 1

If force (F), velocity (V), and time (T) to be the fundamental quantity, then the dimension of the momentum is given as,

⇒  =

  • Hence, option 1 is correct.

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