Question

A rigid body can be hinged on any point on the y-axis. When
the hinge is at y, the moment of inertia is given by
1 = 4y2 - 8y + 6
The y coordinate of COM is (Assume axis is parallel to z-axis)
3
2.​

Answer 1

Step-by-step explanation:

Given:

a rigid body can be hinged about any point on the x-axis. When it is hinged such that the hinge is at a distance x the moment of inertia is given by I=2x

2

−12x+27

To find the x-coordinate of centre of mass

Solution:

Moment of inertia is minimum at the center of mass of the body

For I to be minimum,

dx

dI

=0

⟹

dx

d(2x

2

−12x+27)

=0

Now differentiating with respect ot x, we get

4x−12=0

⟹x=3

Hence the x-coordinate of centre of mass is 3

answer by priyanshi pareek

Answer 2

Answer:

The answer will be 1

Step-by-step explanation:

I = 4y²-8y+6

for I to be minimum

dl/dy=0

⟹

d(4y²-8y+6) =0

Now differentiating with respect to y, we get

8y−8=0

⟹y=1

Hence the y-coordinate of centre of mass is 1

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