AP EAPCET 04-Jul-2022 Shift 1 Paper

distribution of masses is given as m(‌

1

3

)N‌

1

N

Which are placed at x=N
when, N=2,3,4.........
Centre of mass of this discrete.system is given as
X=‌

Σmixi

Σmi

where, Σmi is the total mass, which is given as M. Thus, ‌‌X=‌

Σmixi

M

‌=‌

1

M

‌

∞

∑

n=2

m(‌

1

3

)N‌

1

N

×N
‌=‌

m

M

‌

∞

∑

n=2

(‌

1

3

)N
‌=‌

m

M

(‌

1

32

+‌

1

33

+‌

1

34

⋯⋯‌

1

3∞

)
‌=‌

m

M

×‌

1

9

(1+‌

1

3

+‌

1

32

+‌

1

33

...⋯)
‌=‌

m

M

×‌

1

9

(‌

1

1−‌ 1 3

)
‌(∵Sn=‌

a

1−r

‌ when ‌r<1‌ in G.P series) ‌.
‌=‌

m

M

×‌

1

9

×‌

3

2

=‌

m

6M