Week - 1 - Consistency of Units

Aim:

The challenge is to change the given the measurement into the given units.

Procedure:

System of Units:

A system of units is a set of related units that are used for calculations. For example, in the MKS system, the base units are the meter, kilogram, and second, which represent the base dimensions of length, mass, and time, respectively. In this system, the unit of speed is the meter per second.

Now converting the given measurement into the given units

1. Conversation of Kg cm ms

Mass = 1kg

Length 1m= `10^2`cm

Time 1s = `10^3`ms

Force 1N = `(kg.m)/(s^2)`

= `(kg*10^2 cm)/(10^3 ms^2)`

= `(10^-4 kg*cm)/(ms^2)`

Stress 1Pa = `kg*m`= `N/m^2`

= Newton= `Kg*m*s^-2`

= `(kg*m)/(m^2*s^2)` = `(kg)/(m*s^2)`

= `(kg)/(10^2 cm*10^6 ms^2)`

= `(10^-8 kg)/ (cm*ms^2)`

Energy 1Nm = `(kg*m^2)/s^2`

= `(kg*cm^2)/(10^2ms^2)`

= `(10^-2 kg*cm^2)/(ms^2)`

Density `(1kg)/(s^2)`

= `(kg)/(10^6 cm^3)`

= `(10^-6 kg)/(cm^3)`

Young's Modulus = 210Gpa

`1Gpa = 10^9 pa`

= `(2100kg)/(cm*ms^2)`

Velocity 56.33KMPH =15.64m/s

= `(15.64*10^2 cm)/(10^3 ms)`

=`(1.564 cm)/(ms)`

Gravity `(9.8m)/s^2` = `(9.8 * 10^2cm)/(10^6 ms^2)`

= `(9.8*10^-4 cm)/(ms^2)`

2. Conversation of kg cm s

Mass 1kg = `10^3`g

Length 1m= `10^2`cm

Time 1s = `10^3`ms

Force 1N = `(kg.m)/(s^2)`

= `(kg*10^2 cm)/(s^2)`

Stress 1Pa = `kg*m`= `N/m^2`

= Newton= `Kg*m*s^-2`

= `(kg*m)/(m^2*s^2)` = `(kg)/(m*s^2)`

= `(kg)/(10^2 cm*s^2)`

= `(10^-2 kg)/ (cm*s^2)`

Energy 1Nm = `(kg*m^2)/s^2`

= `(kg*10cm^2)/(s^2)`

= `(10^-2 kg*cm^2)/(s^2)`

Density `(1kg)/(s^2)`

= `(kg)/(10^6 cm^3)`

= `(10^-6 kg)/(cm^3)`

Young's Modulus = 210Gpa

`1Gpa = 10^9 pa`

= `(210*10^9*10^-2 kg)/(cm*s^2)`

= `(210*10^7 kg)/(cm*s^2)`

Velocity 56.33KMPH = 15.64m/s

= `(15.64*10^2 cm)/(s)`

=`(1.564 cm)/(s)`

Gravity `(9.8m)/s^2` = `(9.8 * 10^2cm)/(10^6 ms^2)`

= `(9.8*10^2 cm)/(s^2)`

3. Converting of gm mm ms

Mass 1kg = `10^3`g

Length 1m= `10^3`mm

Time 1s = `10^3`ms

Force 1N = `(kg.m)/(s^2)`

= `(gm*mm)/(ms^2)`

Stress 1Pa = `kg*m`= `N/m^2`

= Newton= `Kg*m*s^-2`

= `(kg*m)/(m^2*s^2)` = `(kg)/(m*s^2)`

= `(`10^3`gm)/(10^3 cm*`10^6`ms^2)`

= `(10^-6 gm)/ (mm*ms^2)`

Energy 1Nm = `(kg*m^2)/s^2`

= `(`10^3gm`*`10^6`mm^2)/(ms^2)`

= `(10^3 gm*mm^2)/(ms^2)`

Density `(1kg)/(s^2)`

= `(`10^3`gm)/(10^9 mm^3)`

= `(10^6 gm)/(ms^3)`

Young's Modulus = 210Gpa

`1Gpa = 10^9 pa`

= `(210*10^9*10^-6 kg)/(mm*ms^2)`

= `(210*10^10`*10^-6` gm)/(mm*ms^2)`

Velocity 56.33KMPH = 15.64m/s

= `(10^3 mm)/(10^3 ms^2)`

=`(15.64 mm)/(ms)`

Gravity `(9.8m)/s^2` = `(9.8 * 10^3mm)/(10^6 ms^2)`

= `(9.8*10^3 mm)/(ms^2)`

The converted values of remaing units

Units	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity	Gravity
Kg cm ms	1 kg	`10^2cm`	`10^3ms`	`(kg.cm)/(10^4ms^4)`	`(10^-8kg)/(cm*ms^2)`	`(10^-2kg*cm^2)/(ms^2)`	`(10^-6kg)/(cm^3)`	`(2100kg)/(cm*ms^2)`	`(1.564cm)/(ms)`	`(9.8*10^-4cm)/(ms^2)`
Kg cm s	1 kg	`10^2cm`	`10^3ms`	`(10^2kg.cm)/(s^2)`	`(10^-2kg)/(cm*s^2)`	`(10^-2kg*cm^2)/(s^2)`	`(10^-6kg)/(cm^3)`	`(210*10^7kg)/(cm*s^2)`	`(1564.7cm)/(s)`	`(9.8*10^2cm)/(s^2)`
gm mm ms	`10^3` kg	`10^3mm`	`10^3ms`	`(gm.mm)/(ms^2)`	`(10^-6gm)/(mm*ms^2)`	`(10^-3gm*mm^2)/(ms^2)`	`(10^-3gm*mm^2)/(ms^3)`	`(21*10^4gm)/(mm*ms^2)`	`(15.64m)/(ms^2)`	`(9.8*10^3m)/(ms^2)`
kg m s	`1 kg`	`1 m`	`1 s`	`(1 kg.m^2)/(s^2)`	`(1 kg)/(m*s^2)`	`(1 kg*m^2)/(s^2)`	`(kg)/(m^3)`	`(210*10^9 kg)/(m^2)`	`(15.64m)/(s)`	`(9.8m)/(s^2)`
g cm s	`10^3` kg	`10^2cm`	`1 s`	`(10^5gm.cm^2)/(s^2)`	`(10kg)/(cm*s^2)`	`(10^-7 gm*cm)/(s^2)`	`(10^-5 gm)/(cm^3)`	`(210*10^10gm)/(cm*s^2)`	`(1564.7cm)/(s)`	`(9.8*10^2cm)/(s^2)`
g cm us	`10^3 g`	`10^2cm`	`10^3 us`	`(10^7g*cm)/(us^2)`	`(10^-11g)/(cm*us^2)`	`(10^-5g*cm^2)/(us^2)`	`(10^-3g)/(cm^3)`	`(210*10^-3g)/(cm*us^2)`	`(15.64*10^-4cm)/(us)`	`(9.8*10^-10cm)/(us^2)`
g mm s	`10^3 g`	`10^3mm`	`10^3ms`	`(10^6 g.mm)/(s^2)`	`(g)/(mm*s^2)`	`(10^9 g*mm^2)/(s^2)`	`(10^-6g)/(mm^3)`	`(210*10^9 g)/(mm*s^2)`	`(15.64*10^3mm)/(s)`	`(9.8*10^3mm)/(s^2)`
ton mm s	`10^3 g`	`10^3mm`	`1 s`	`(ton*mm)/(s^2)`	`(10^-6 ton)/(mm*s^2)`	`(10^3 ton*mm^2)/(s^2)`	`(10^-2 ton)/(mm^3)`	`(210*10^3 ton)/(mm*s^2)`	`(1564*10^3mm)/(s)`	`(9.8*10^3mm)/(s^2)`
slug ft s	`0.0685 slug`	`3.2808 ft`	`1 s`	`(0.2247slug*ft)/(s^2)`	`(0.02087slug)/(ft*s^2)`	`(0.7373slug*ft^2*cm^2)/(s^2)`	`(1939*10^-3slug)/(ft^3)`	`(4.384*10^9slug)/(ft*s^2)`	`(51.33ft)/(s)`	`(32.151ft)/(s^2)`
kg mm s	1 kg	`10^3mm`	`1s`	`(kg.10^3mm)/(s^2)`	`(10^-3kg)/(mm*s^2)`	`(kg*10^6mm^2)/(s^2)`	`(10^-9kg)/(mm^3)`	`(210*10^6kg)/(mm*s^2)`	`(15.64*10^3mm)/(s)`	`(9.8*10^3mm)/(s^2)`
g cm ms	`10^3 g`	`10^2cm`	`10^3ms`	`(10^-1g.cm)/(ms^2)`	`(10^-5g)/(cm*ms^2)`	`(10g*cm^2)/(ms^2)`	`(10^-6g)/(cm^3)`	`(210*10^6g)/(cm*ms^2)`	`(15.64*10^-1cm)/(ms)`	`(9.8*10^-4cm)/(ms^2)`
kg mm ms	1 kg	`10^3mm`	`10^3ms`	`(10^-3kg.mm)/(ms^2)`	`(10^-9kg)/(mm*ms^2)`	`(kg*mm)/(ms^2)`	`(10^-9kg)/(mm^3)`	`(210kg)/(mm*ms^2)`	`(15.64mm)/(ms)`	`(9.8*10^-3mm)/(ms^2)`

Result:

Hence the measurement has been converted to the respective unit.