Answer
Verified
389.7k+ views
Hint: We know that the force causes a body to move. Also, the unit of motion is generally, \[N\] when the mass of the body is in \[kg\], distance is in $m$ and time is in $s$. Here, these quantities are changed in order to find a new force.
Formula used: \[F={{M}^{1}}{{L}^{1}}{{T}^{-2}}\],where $M$ is the mass, $L$ is the length and $T$ is the time.
Complete step-by-step solution:
Given that the new units are, $F=1KN=1000N$, $L=1km=1000m$ and $T=100s$
We know that $F=ma$, where $m$ is mass and $a$ is acceleration.
We also know that the dimension of force is given as \[F={{M}^{1}}{{L}^{1}}{{T}^{-2}}\], where $M$ is the mass, $L$ is the length and $T$ is the time.
We can substitute the given values to find the unknown dimension, here $M$.
Then we get, $1000=\dfrac{M\times 1000}{100^{2}}$
Or we get $M=100^{2}=10000kg$
Hence the answer is (C.) \[10,000kg\]
Additional information:
Dimensional analysis is the relationship between different physical quantities. The physical quantities are expressed in terms of the basic quantities like mass, length, and time. These basic quantities are raised to their specific powers to represent the physical quantity.
This method is all called the factor-label method or unit-factor method. This method was found by Joseph Fourier in the year 1822. There are also a few constants called dimensionless quantities. These as the name suggests do not have any dimensions or units.
Note: Dimensions are different form units. There can be different units for the same dimension. For eg: say the dimension is length, then the different units are millimeters, centimeters, meters, kilometers, yards, inch, foot, a mile, and so on. There can also be dimensions without units, called the dimensionless quantity.
Formula used: \[F={{M}^{1}}{{L}^{1}}{{T}^{-2}}\],where $M$ is the mass, $L$ is the length and $T$ is the time.
Complete step-by-step solution:
Given that the new units are, $F=1KN=1000N$, $L=1km=1000m$ and $T=100s$
We know that $F=ma$, where $m$ is mass and $a$ is acceleration.
We also know that the dimension of force is given as \[F={{M}^{1}}{{L}^{1}}{{T}^{-2}}\], where $M$ is the mass, $L$ is the length and $T$ is the time.
We can substitute the given values to find the unknown dimension, here $M$.
Then we get, $1000=\dfrac{M\times 1000}{100^{2}}$
Or we get $M=100^{2}=10000kg$
Hence the answer is (C.) \[10,000kg\]
Additional information:
Dimensional analysis is the relationship between different physical quantities. The physical quantities are expressed in terms of the basic quantities like mass, length, and time. These basic quantities are raised to their specific powers to represent the physical quantity.
This method is all called the factor-label method or unit-factor method. This method was found by Joseph Fourier in the year 1822. There are also a few constants called dimensionless quantities. These as the name suggests do not have any dimensions or units.
Note: Dimensions are different form units. There can be different units for the same dimension. For eg: say the dimension is length, then the different units are millimeters, centimeters, meters, kilometers, yards, inch, foot, a mile, and so on. There can also be dimensions without units, called the dimensionless quantity.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE