Velocity of a particle at time t is given by v=at+(b)/(t+c)a,b, care constant. The dimension of a b, c will be ......

Velocity of a particle at time t is given by v=at+(b)/(t+c)a,b, care c

1.	Velocity of a particle at time t is given by v=at+(b)/(t+c)a,b, care constant. The dimension of a b, c will be ......
Answer» `L^(2),T and LT^(-2)` `LT^(2),LT and L` `L,LT and T^(2)` `LT^(2), L and T` SOLUTION :`v=at+(b)/(t+C)` Hence both term on RIGHT hand SIDE should have dimension of velocity. `:.v=at` `:.a=(v)/(t)` `:.[a]=([v])/([t])` `=(LT^(-1))/(T)` `=LT^(-2)`By homogeneity indicate, and `v=(b)/(t+c)=(b)/(t) "" t+c`(has dimension of time) `:.b=vt "" c=t` `:.[b]=[v][t] :. [c]=[t]` `=(LT^(-1))(T) "" :. c=T` `=L` `:.[a],[b],[c]=LT^(-2), L and T`