If the force is given by F = at + bt2 with t as time. The dimensions of a and b are

Question

If the force is given by F = at + bt2 with t as time. The dimensions of a and b are (A) [MLT-4] and [MLT-2] (B) [MLT-3] and [MLT-4] (C) [ML2T-3] and [ML2T-2] (D) [ML2T-3] and [ML3T-4]

Tardigrade Admin · Accepted Answer

Dimension of at = Dimension of F [at] = [F] ⇒ [a] = [(F/t)] [b] = [(MLT-2/T)] ⇒ [a] = [MLT-3] Dimension of bt2 = Dimension of F [bt2] =[F] [b] =[(F/t2)] [b] = [(MLT-4/T2)] ⇒ [b] = [MLT-4]

Q. If the force is given by $F = a t + b t^{2}$ with $t$ as time. The dimensions of $a$ and $b$ are

$[M L T^{- 4}]$ and $[M L T^{- 2}]$

$[M L T^{- 3}]$ and $[M L T^{- 4}]$

$[M L^{2} T^{- 3}]$ and $[M L^{2} T^{- 2}]$

$[M L^{2} T^{- 3}]$ and $[M L^{3} T^{- 4}]$

Q. If the force is given by F=at+bt2 with t as time. The dimensions of a and b are

[MLT−4] and [MLT−2]

[MLT−3] and [MLT−4]

[ML2T−3] and [ML2T−2]

[ML2T−3] and [ML3T−4]

Dimension of at= Dimension of F [at]=[F] ⇒[a]=[tF​] [b]=[TMLT−2​] ⇒[a]=[MLT−3] Dimension of bt2 = Dimension of F [bt2]=[F][b]=[t2F​] [b]=[T2MLT−4​] ⇒[b]=[MLT−4]

Q. If the force is given by $F = a t + b t^{2}$ with $t$ as time. The dimensions of $a$ and $b$ are

$[M L T^{- 4}]$ and $[M L T^{- 2}]$

$[M L T^{- 3}]$ and $[M L T^{- 4}]$

$[M L^{2} T^{- 3}]$ and $[M L^{2} T^{- 2}]$

$[M L^{2} T^{- 3}]$ and $[M L^{3} T^{- 4}]$