Question

which of the following relation is not dimensionally correct? (k- kinetic energy, m-mass, v-speed,h-height, g-acceleration due to gravity)
a)k=m²v³
b)K=mv²
c)k=(3/16)mv²
d)k=mgh​

Answer 1

Kinetic energy and potential energy have same dimensions d) k=mgh​

Explanation for the correct option:

Dimensions for kinetic energy

• Formula for kinetic energy is 1/2mv^2
• For according to dimentions, we don't have any dimension for the digits. Whereas, M=mass, v=speed/velocity.
• So, k=[M][V]^2
• But velocity = distance/time and L=distance, T= time. So, dimention of velocity become [LT^-1]
• Putting value of velocity in above formula, we get
• K= [M][L]^2[T]^-2

Dimensions for potential energy

• Formulas for potential energy is P=mgh
• where g=ms^-2
• Putting the value of dimensions
• [M][L][T]^-2[L]
• P=[M][L]^2[T]^-2

Hence, option d) k=mgh​ is correct

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