{"id":5652,"date":"2019-11-03T12:40:32","date_gmt":"2019-11-03T07:10:32","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5652"},"modified":"2022-11-04T12:06:29","modified_gmt":"2022-11-04T06:36:29","slug":"dimension-of-force","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/dimension-of-force\/","title":{"rendered":"What is the Dimension of Force"},"content":{"rendered":"\n

Dimensional Formula of Force<\/span> with its Derivation<\/span><\/h2>\n\n\n\n

In this article, we will find the dimension of Force<\/p>\n\n\n\n

Dimensional formula for is<\/p>\n\n\n\n

$[M^1L^1T^{-2}]$<\/p>\n\n\n\n

Where
M<\/strong> -> Mass<\/p>\n\n\n\n

L<\/strong> -> Length<\/p>\n\n\n\n

T<\/strong> -> Time
We would now derive this dimensional formula.<\/p>\n\n\n\n

Derivation for expression of Dimension of<\/h3>\n\n\n\n

As per second laws of Newton law’s, Force is defined as the product of mass and acceleration
$F= ma$
Where m -> Mass of the body
a -> Acceleration of the body<\/p>\n\n\n\n

Now the dimension of Mass = $[M^1]$<\/p>\n\n\n\n

Lets derive the dimension of Acceleration
Now
$a = \\frac {\\Delta v}{t}$
Now dimension of Velocity= $[M^0 L^1T^{-1}]$
dimension of Time = $[M^0 T^1]$
So dimension of Acceleration = $ \\frac {[M^0 L^1T^{-1}]}{ [M^0 T^1]}= [M^0 L^1T^{-2}]$
Hence Dimension of force is given by<\/p>\n\n\n\n

$\\text {Dimension of Force} =[M^1] \\times [M^0 L^1T^{-2}] = [M^1L^1T^{-2}]$<\/p>\n\n\n\n

Unit of Force is Newton<\/p>\n\n\n\n

Try the free Quiz given below to check your knowledge of Dimension Analysis:-<\/p>\n\n\n\n

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Quiz on Dimensional Analysis<\/strong><\/span><\/h4>\n
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