Question

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Answer 1

GIVEN

• Radius of the spherical body = r
• Velocity of the spherical body = v
• Coefficient of viscosity of the fluid = η
• Force of viscosity acting on the spherical body = F

TO FIND

An expression for F using method of dimensions.

WE MUST KNOW

Force of viscosity acting on a spherical body of radius r moving with velocity v through a fluid of viscosity η is given by  :-

F = 6 π η r v

SOLUTION

F = 6 π η r v

Dimensionally,

$\sf{F=ML^{-1}T^{-1}\times L \times LT^{-1}}\\\\\sf{\longrightarrow F=ML^-^1\times L \times L \times T^-^1 \times T^-^1}\\\\\underline{\boxed{\boxed{\sf{F=MLT^-^2}}}}\:\:\:\: \cdots \mathbf{ANSWER}$

Therefore, the expression for F using method of dimensions here, is MLT⁻².

Answer 2

Given

Force of viscosity F acting on a spherical body moving through a fluid depends upon its velocity (v) radius (r) and co-efficient of viscosity ' η ' of the fluid . Using method of dimensions obtain an expression for 'F'

Solution

• Radius = r
• Velocity = v
• Coefficient of viscosity of the fluid=η
• Force acting on spherical body = F

As we know that

F = 6 π η r v

$\implies\sf F=ML^{-1}T^{-1}\times{L}\times{LT^-1}$

$\implies\sf F=ML^{-1}\times{L}\times{L}\times{T^{-1}}\times{T^{-1}}$

$\sf \red{\boxed{So,\: dimension\:for\:''F''=MLT^{-2}}}$