A long beam is spun at a costant speed of 1.75 rad /s During the period of training an astronaut is made to walk slowly along this beam , away from the axis of rotation At what distance , from the axis of rotation , he will experience a centrifugal acceleration equal to the acceleration due gravity ?

Options

A. `3.2 m`
B. `1.6m`
C. `0.8m`
D. `6.4m`

Answer

A

Explanation

`omega = 1.75 rad //s = (7)/(4) rad//s `
When he is at a distance x from the axis of rotation , he will experience a ,C.P acceleration (a)
where `a= x omega ^(2)`
It is given that ` x omega ^(2) ` = g
` therefore x= (g )/(omega ^(2)) =(9.8 )/((7)/(a)xx(7)/(4))=(9.8xx4xx4)/(49)` ,
` therefore x=16 xx0.2=3.2 m`