The SI unit of energy is 
, that of speed v is 
and of acceleration a is 
.
Which of the formula for kinetic energy (K) given below can you rule out on the basic of dimensional arguments (m stands for the mass of the body)?
(I) 
(II) 
(III) 
(IV) 
(V) 
Text Solution
Verified by ExpertsD
The dimensions of the quantity on the right side are 
for (I): 
for (II) and
(IV): 
for (III).
The quantity on the right side of 
has no proper dimensions since, two quantities of different dimensions have been added. Since, the kinetic energy 
has the dimensions of 
, formulas (I), (III) and (V) and ruled out. The correct dimensions for kinetic energy is given by (II) and (IV).
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