Physics, asked by mariasattar2002, 3 months ago

center of mass of a semi circular lamina of radius a whose density varies as square of distance from center is ?

Answers

Answered by apurba2004vizag
0

Answer:

As the wire is uniform, the mass per unit length of the wire is  

πR

M

​  

. The mass of the element is, therefore,

dm=(  

πR

M

​  

)(Rdθ)=  

π

M

​  

The coordinates of the center of mass are

X=  

M

1

​  

∫xdm=  

M

1

​  

∫  

0

π

​  

(Rcosθ)(  

π

M

​  

)dθ=0

Y=  

M

1

​  

∫ydm=  

M

1

​  

∫  

0

π

​  

(Rsinθ)(  

π

M

​  

)dθ=  

π

2R

​  

 

Hence, position of center of mass, (0,  

π

2R

​  

)

Explanation:

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