Question

The variation of density of a cylindrical thick and
long rod, is d = d'x^2/L^2,
then position of its centre
of mass from x = 0 end is :-
(1) 2L/3 (2) L/2 (3) L/3 (4) 3L/4​

Answer 1

Answer:

ANSWER

Let the width of disc at a distance x is dx and the radius of the cylinder is r.

The mass of the disc is given as,

dm=πr

2

dx×

L

2

ρ

0

x

2

The centre of mass is given as,

CM=

∫

0

L

dm

∫

0

L

xdm

=

∫

0

L

πr

2

dx×

L

2

ρ

0

x

2

∫

0

L

πr

2

dx×

L

2

ρ

0

x

3

=

∫

0

L

x

2

dx

∫

0

L

x

3

dx

=

3

L

3

4

L

4

=

4

3L

Thus, the position of centre of mass from x=0 end is

4

3L

.