Question

dimensions of kinetic energy are the same as that of
a) force
b) acceleration
c) work
d) pressure​

Answer 1

Answer:

(c) work............ M L 2 T-2

Answer 2

Answer:

Work

Explanation:

The kinetic energy of an object is given by :

$E_k=\dfrac{1}{2}\times m\times v^2$

The dimensional formula of $[m] = [M]$

The dimensional formula of $[v] = [LT{-1}]$

So, the dimensional formula of kinetic energy, $[E_k]=[ML^2T^{-2}]$

Force required of an object is given by :

$F=m\times a$

The dimensional formula of Force, $[F]=[MLT^{-2}]$

The dimensional formula of acceleration, $[a]=[LT^{-2}]$

Work done is given by :

$W=F\times d$

The dimensional formula of work done is $[W]=[ML^2T^{-2}]$

The formula of pressure is given by :

$P=\dfrac{F}{A}$

The dimensional formula of pressure is, $[P]=[ML^{-1}T^{-2}]$

So, the dimension of kinetic energy is same as work. Hence, the correct option is (c).