A student writes the relation for the distance travelled by a body moving with…

PHYSICS · Single correct · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

A student writes the relation

s = u t + \dfrac{1}{2} a t

for the distance

s

travelled by a body moving with initial velocity

u

under uniform acceleration

a

for time

t

. Which statement correctly explains why this relation is dimensionally wrong? (a) The factor

\dfrac12

alters the dimensions of the term

\dfrac12 a t

, so the equation becomes inconsistent. (b) Both terms on the right have dimensions of velocity only. (c) The term

\dfrac12 a t

does not have the same dimensions as

s

. (d) The dimension of acceleration

a

is taken as

L T^{-1}

, so

a t

is length while

u t

is velocity; hence the two terms cannot be added.