Question

.GOOD MORNING
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Q. no. 6
.Give the solution with full explanations ​​

Answer 1

⭐《ANSWER》

$\huge\mathfrak\pink {ANSWER}$

↪Actually welcome to the concept of the DIMENSIONAL ANALYSIS

↪Basically , we know that here ,

↪KINETIC ENERGY is always , 1/2 m v^2

↪so here , equating the dimensions and getting required Answer

Answer 2

Answer.......

• The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speed ω .

• Assuming relation to be K= kIᵃωᵇ

• k is a dimensionless constant, find a and b.

• Moment of inertia of a sphere of the diameter

Here....

K= kIᵃωᵇ

• k is the kinetic energy of any rotating body also a dimensionless constant.

• Dimension of Kinetic energy, K= [ML²T⁻²]

• Dimension of Moment of Inertia is Iᵃ = [ML²]ᵃ

• Dimension of angular speed is ωᵇ = [T⁻¹]ᵇ

• principle of homogeneity of dimension.

• dimension in eq (i)

[ML²T⁻²] = [ML²]ᵃ

2=2a ; -b=-2 (L²=L²ᵃ & T⁻²=T⁻ᵇ)

p a=1 ; b= 2