Question

15. A uniform semi-circular wire of radius 1 m and
unknown mass is lying in xy plane as shown. The
coordinate of its centre of mass are (in m)

options are :-
1) ( 0 , 1/π )
2) ( 0 , 2/π )
3) ( 1/π , 0 )
4) ( 2/π , 0 )


plz solve it quikly , its very urgent , plz dont give wrong answers if u dont know plz plz​

Answer 1

Answer:

For a semicircular ring having some non zero mass, the coordinate of centre of mass when the radius is R

is

x coordinate = Abcissa of the centre of the semicircular ring

y-coordinate = 2R/π above the centre of the circle

This can be easily proved by using the formula

y (com) = Integral of y dm/ Integral of dm

where, dm is an infinitesinally small mass element.

So,

Because here the radius of the semicircular ring is 1 m.

Therefore, the coordinates of the centre of mass of given wire will be

(0,2(1)/π) = (0,2/π)