Question

A 100 kg (220 lb) person stands on a 1 m diameter platform and raises a 1000 kg (2200 lb) car. What is the least diameter of the platform the car is on?

Answer 1

The minimum diameter of other platform is 3.162 meters.

Step-by-step explanation:

We shall use Principle of transmission of pressure to solve the problem

The Principle of transmission of pressure states that any increase in pressure in a fluid is increased throughout the whole fluid

Mathematically we have

Increase in pressure due to person of mass 100 kg standing on a platform of diameter 1 meter equals

`P_(1)=(F)/(Area)=(mg)/((\pi)/(4)d_(1)^(2))\\\\\therefore P_(1)=(4* 100* g)/(\pi * (1)^(2))...............(i)`

The increase in pressure shall be equal to the pressure applied to the car

Thus to just raise the car we have

`P_(1)* A_(2)=W_(car)`

where

`A_(2)` is the area of platform 2

thus equating the values we get

`(4* 1000* g )/(\pi * d^(2))=(4* 100* g)/(\pi * 1^(2))\\\\\therefore d^(2)=10\\\\\therefore d=√(10)=3.162meters`