Question

A force is given by F=at+bt² where t' is the time. The dimensions of a and b are.​

Answer 1

SOLUTION-;

⇒  Since F=at+bt 2  −−−(1)

∴ Dimension of at and bt  2

 must be equal to force only.

Hence [F]=[M  1  L  1  T  −2  ]−−−(2)

F from (1) and (2)  

⇒ [at]=a[T]=[F]

∴ a[T]=[M  1  L  1  T  −2  ]

∴ [a]=[M  1  L  1  T  −3  ]  

and per bt  2  =b[T  2  ]=[M  L  1  T  −2 ] ∴   [b]=[M  1  L  1  T  −4

]

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