The velocity of a body is given by the equation v=(b/t)+ct2+dt3 The dimensional formula of b is

Question

The velocity of a body is given by the equation v=(b/t)+ct2+dt3 The dimensional formula of b is (A) [M0LT0] (B) [M0L0T0] (C) [M0L0T] (D) [MLT-1]

Tardigrade Admin · Accepted Answer

In the equation, left hand side has the dimension of velocity. Then from the principle of homogeneity each term in the right-hand side should have the dimensions of velocity [(b/t)]=[v] or [b]=[vt]=[L]

Q. The velocity of a body is given by the equation $v = \frac{b}{t} + c t^{2} + d t^{3}$ The dimensional formula of $b$ is

$[M^{0} L T^{0}]$

$[M^{0} L^{0} T^{0}]$

$[M^{0} L^{0} T]$

$[M L T^{- 1}]$

In the equation, left hand side has the dimension of velocity. Then from the principle of homogeneity each term in the right-hand side should have the dimensions of velocity $[\frac{b}{t}] = [v]$ or $[b] = [v t] = [L]$

Q. The velocity of a body is given by the equation v=tb​+ct2+dt3 The dimensional formula of b is

[M0LT0]

[M0L0T0]

[M0L0T]

[MLT−1]