Question

plz help me in this question ​

Answer 1

(1) if the error in radius is 3% what is the error in volume of sphere

error in radius = 3%

$\frac{ \Delta \: r}{r} \times 100 = 3$

Volume of sphere (V )= 4π R ³ /3

As per error formula ,

$\frac{ \Delta \:v }{v} \times 100 = 3 \frac{ \Delta \: r}{r} \times 100$

$\frac{ \Delta \:v }{v} = 3 \frac{ \Delta \: r}{r}$

$\frac{ \Delta \:v }{v} = 3 \times 3$

$\boxed{\frac{ \Delta \:v }{v} = 9}$

(2)Find dimension of coefficient of viscosity

The coefficient of viscosity is a measure of resistance to the flow of liquid

viscosity is given by the formula,

$F = 6\pi \eta \: rv$

here ,

• F = viscous force
• n = coefficient of viscosity
• r = radius of sphere
• v = velocity of sphere

Dimensionless =6π

Dimension of r = [L ¹]

Dimension of v

= distance / time

= [ L ¹] / [T ¹]

= [ L¹ T ^-1]

Dimension of Force

= m a

mass = [ M ¹]

acceleration

= Velocity / time

= [ L¹ T ^-2]

Dimension of Force

= [ M ¹] [ L¹ T ^-2]

= [ L¹ M ¹ T ^-2]

$\eta = \frac{F}{rv}$

$\eta = \frac{ {L}^{1} {M}^{1} {T}^{ - 2} }{{L}^{1} \times {L}^{1}{T}^{ - 1} }$

$\boxed{ \eta = {L}^{ - 1} {M}^{1} {T}^{ - 1} }$