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

Answer:

Option C is right

Explanation:

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Answer 2

Given :  K→kinetic energy, m→mass, v→speed, h→height, g→acceleration due to gravity

To Find : Which of the following relation is not dimensionally correct

Solution:

kinetic energy  and potential energy both has units of dimensions

KE = ( 1/2)mv²

PE = mgh

Hence Dimensionally

K can  be   =  A *  ( 1/2)mv²     where A is a dimensionless constant

or K can be  A * mgh

K = mv²   = 2 * ( 1/2)mv²   Hence Dimensionally  correct

K = (3/16)mv²  = (3/8) * ( 1/2)mv²   Hence Dimensionally  correct

K = mgh​  = 1  * mgh  Hence Dimensionally  correct

k = m²v³   is  not Dimensionally correct

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