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

Answer:

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

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

$y_{com}=\frac{m_1y_1+m_2y_2}{m_1+m_2}$

Now since it is given that $y_{com}=1.3$

Applying the given values in the above relation we get

$1.3=\frac{1000\times y_1+500\times 1.8}{1000+500}$

Solving for $y_1$ we get

$1000y_1=1.3\times 1500-500\times 1.8\\\\1000y_1=1050\\\\\therefore y_1=\frac{1050}{1000}=1.05m$