MATHEMATICS: Ratio, Proportion, Variation - Force of Gravitation, Weight, surface Illumination intensity, current, resistance

WEIGHT is inversely proportional to the SQUARE OF R

where:

WEIGHT = force of attraction between the Earth and an object

R = distance of object from the center of the Earth


example:

A satellite weighs 700 N (Newtons) on the surface of the Earth. How much will the satellite weigh at an altitude of 250 km above the Earth's surface. Take the radius of the Earth as 4000 miles.


given:

W1 = 700 N

R1 = 4000 mi

R2 = 4000 + 250

R2 = 4250


find:

W2 = weight of satellite at an altitude of 250 km above the Earth


solution:


W = k/R^2

k = W * R^2

W1 * (R1)^2 = W2 * (R2)^2

700 * (4000)^2 = W2 * (4250)^2

W2 = 700 * (4000)^2/(4250)^2

W2 = 700 * 16,000,000/18,062,500

W2 = 620 N  ---> the satellite is lighter




INTENSITY OF SURFACE ILLUMINATION is inversely proportional to the SQUARE OF THE DISTANCE BETWEEN THE SOURCE AND THE SURFACE


example:

A certain light source has an illumination of 700 lux (lumens per square meter) on a surface. If the distance is doubled, find the resulting illumination.


given:

I1 = 700 lux

d1 = initial distance

d2 = 2 * d1


find:

I2 = surface illumination when the distance is doubled



solution:


I = k/d^2

k = I * d^2

I1 * (d1)^2 = I2 * (d2)^2


700 * (d1)^2 = I2 * (2 * d1)^2

700 * (d1)^2 = I2 * 4 * (d1)^2

I2 = 700/4

I2 = 175 lux  ---> reduced to 1/4 or 25% of the initial illumination





ELECTRIC CURRENT is inversely proportional to CIRCUIT RESISTANCE


example:

When the resistance of a circuit is increased by 10%, by what percent will the current change?


given:

R1 = initial circuit resistance

R2 = 1.10 R1

I1 = initial current


find:

I2 = current when resistance is increased by 10%


solution:


I = k/R

k = I * R

I1 * R1 = I2 * R2

I1 * R1 = I2 * 1.10 R1 

I1 = 1.10 I2  ---> equation 1



%I = [(I2 - I1)/I1] * 100%


substituting from equation 1,

%I = [(I2 - 1.10 I2)/1.10 I2] * 100%

%I = [-0.10/1.10] * 100%

%I = -9.09 % (negative value means decrease)

%I = 9.09 % decrease in Electric current