Question

A hollow hemisphere and a solid hemisphere of equal radius and mass are placed as shown , the coordinates of their mutual center of mass are???

pls answer......
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Answer 1

Answer:

X co-ordinate = -R/16

Y co-ordinate = 0

( -R/16 , 0 )

Explanation:As they have equal mass we'll let mass be 'm'.

The Y1 and Y2 co-ordinates will be zero cause the center of masses of both the objects are on x axis.

Now according to the formula the distance of center of mass of solid hemisphere is R/2

Thus, X1 = 3R/8

Now according to the formula the distance of center of mass of hollow hemisphere is 3R/8

Thus, X2 = -R/2

(minus sign cause the center of mass of this hemisphere is on the left side)

Now according to the formula,

= m(X1) - m(X2) / m + m

= m(3R/8) - m(R/2) / 2m

= m ( 3R/8 - R/2 ) / 2m

(Cancelling 'm' from numerator and denominator)

= ( 3R/8 - R/2 ) / 2

= ( 3R/8 - 4R/8) / 2

= ( -R/8 ) / 2

= -R/16

The Y1 and Y2 coordinates are zero so the answer for Y co-ordinate will also be zero.

This is the final answer.

Hope I helped :)

( this is my first time )