The displacement of a particle moving along x-axis with respect to time t is x=at+bt2−ct3x = at + b t ^ 2 - c t ^ 3x=at+bt2−ct3. The dimensions of c are 1)T−3T^{-3}T−3, 2)LT−2L T ^ {- 2}LT−2, 3)LT−3LT^{-3}LT−3, 4)LT3LT^{3}LT3, 5)LT2LT^{2}LT2,

Question:

The displacement of a particle moving along x-axis with respect to time t is $x = at + b t ^ 2 - c t ^ 3$ . The dimensions of c are

T^{-3}

L T ^ {- 2}

LT^{-3}

LT^{3}

LT^{2}

Solution:

Verified

Answer (3)

Given,

$x=at+bt^2-ct^3$

$\displaystyle \therefore [ct^3]=[x]$

$\displaystyle \Rightarrow [c]=\frac {[x]} {[t^3]} =\frac {[L]} {[T^3]}=[LT^{-3}]$