Question

A man is 1.8 m tall and weighs 1000 N. He lifts a 500 N weight to the top of his head. If the C.G. of the man plus weight is now 1.3 m above the ground, how high is the C.G. of the man alone?

Answer 1

The C.G of the man is 1.05 meters above the ground.

Step-by-step explanation:

Let the co-ordinate of the man be
`'y_1'`

We know that C.G of combined system of masses
`m_1,m_2` having individual co-ordinate od C.G as
`y_1,y_2` is

`y_(com)=(m_1y_1+m_2y_2)/(m_1+m_2)`

Now since it is given that
`y_(com)=1.3`

Applying the given values in the above relation we get

`1.3=(1000* y_1+500* 1.8)/(1000+500)`

Solving for
`y_1` we get

`1000y_1=1.3* 1500-500* 1.8\\\\1000y_1=1050\\\\\therefore y_1=(1050)/(1000)=1.05m`