Question

show that kinetic energy amd potentional energy are dimensioally similar

Answer 1

Answer:

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Explanation:

Kinetic energy is given by half the product of mass and velocity squared.

KE=12mv2

Dimension for mass is M1L0T0 , and the dimensional formula for velocity is M0L1T−1

So, the dimensional formula for KE is

M1 × (M0L1T−1)2

Giving us

M1L2T−2

Gravitational potential energy is given by the product of mass, gravitational acceleration and height, in its simplified form anyways.

PEg=mgh

The dimensional formula for mass is, again, M1L0T0 , the dimensional formula for gravitational acceleration is M0L1T−2 , and for height, it is M0L1T0 .

So the dimensional formula for potential energy is given by

M1L0T0 × M0L1T−2 × M0L1T0

Giving us

M1L2T−2

Which is the same as kinetic energy, which makes sense. They're both given in units of joules.

Work is also given in units of joules and is equal to kinetic energy, therefore also has the same dimensional formula.

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