Answer
Verified
377.4k+ views
Hint: In order to find the dimensional formula of velocity, we need to know the formula of velocity i.e., velocity, $v = \dfrac{s}{t}$ where $s = $displacement, $t = $time taken.
Then we need to find units of velocity, displacement and time in the terms of fundamental quantities.
Complete step-by-step solution:
Fundamental quantities: The quantities which are independent of any other quantities are called fundamental quantities.
Dimensional formula: The expression showing the relationship between the fundamental quantities and expressing the powers of fundamental quantities to be raised to obtain one unit of derived quantity is called dimensional formula.
E.g., let $K$be a quantity then it’s dimensional formula=${[M]^a}{[L]^b}{[T]^c}$where $M = $mass, $L = $Length and $T = $time
Now, Velocity, $v = \dfrac{s}{t} - - (i)$
SI unit of displacement, $s = m$(meter), \[t = \]$s$(Second)
Substituting the above value in equation$(i)$ we get:
$ v = \dfrac{m}{s} \\
v = m{s^{ - 1}} \\ $
Thus, SI unit of velocity is $m{s^{^{ - 1}}}$
In dimensional formula we represent metre as $M$, second as $S$
So,
Dimensional Formula of velocity=$\left[ M \right]{\left[ T \right]^{ - 1}}$
Final answer:
The dimensional formula of velocity is $\left[ M \right]{\left[ T \right]^{ - 1}}$
Note: There are $7$fundamental quantities that don’t depends on other quantities are as follows:
Mass (Kilogram)
Time (seconds)
Length (metre)
Temperature (kelvin)
Luminous intensity (candela)
Amount of substance (mole)
Electric current (ampere)
Then we need to find units of velocity, displacement and time in the terms of fundamental quantities.
Complete step-by-step solution:
Fundamental quantities: The quantities which are independent of any other quantities are called fundamental quantities.
Dimensional formula: The expression showing the relationship between the fundamental quantities and expressing the powers of fundamental quantities to be raised to obtain one unit of derived quantity is called dimensional formula.
E.g., let $K$be a quantity then it’s dimensional formula=${[M]^a}{[L]^b}{[T]^c}$where $M = $mass, $L = $Length and $T = $time
Now, Velocity, $v = \dfrac{s}{t} - - (i)$
SI unit of displacement, $s = m$(meter), \[t = \]$s$(Second)
Substituting the above value in equation$(i)$ we get:
$ v = \dfrac{m}{s} \\
v = m{s^{ - 1}} \\ $
Thus, SI unit of velocity is $m{s^{^{ - 1}}}$
In dimensional formula we represent metre as $M$, second as $S$
So,
Dimensional Formula of velocity=$\left[ M \right]{\left[ T \right]^{ - 1}}$
Final answer:
The dimensional formula of velocity is $\left[ M \right]{\left[ T \right]^{ - 1}}$
Note: There are $7$fundamental quantities that don’t depends on other quantities are as follows:
Mass (Kilogram)
Time (seconds)
Length (metre)
Temperature (kelvin)
Luminous intensity (candela)
Amount of substance (mole)
Electric current (ampere)
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE