Mechanical Engineering: Centre of the Gravity Online Test

The moment of inertia of a thin spherical shell of mean radius 0.5 m and mass 20 kg about diameter as axis would be
2.5 kg m2
3.33 kg m2
5 kg m2
2.0 kg m2
The moment of inertia of a solid sphere of radius of 0.5 m and mass 50 kg with respect of diametral axis would be
2.5 kg m2
5 kg m2
8.33 kg m2
12.5 kg m2
The radius of gyration of a solid sphere of radius r with respect to diametral axis is
r2/5
2r2/5
r2/2
4 r2/5
The length to radius ratio l/r of a solid cylinder such that the moments of inertia about the longitudinal and transverse axis are equal is
1
2
The moments of inertia of a solid circular section of radius r and of a hollow circular section of radii R and r, each about the diametral lines, are equal. Then
R = 2r
R = 4r
Consider a circular cylinder of mass m, radius r and length l. The moment of inertia with respect to central longitudinal axis would be
m r2/2
m r2/3
m r2/6
m r2/12
The moment of inertia of a thin spherical shell of mass m and radius r about diameter as an axis is
1 m r2 2
m r2
2 m r2 3
2 m r2 5
The moment of inertia of a solid sphere of mass m and radius r with respect to any diameter is
1 m r2 2
m r2
2 m r2 3
5 m r2 4
The moment of inertia of a thin circular ring with radius r and mass m about an axis through its centre and perpendicular to its plane would be
mr2
1 m r2 2
3 m r2 2
5 m r2 4
The moment of inertia of a sphere of mass m and radius r about diameter as axis is given by
2 m r2 3
2 m r2 5
1 m r2 2
3 m r2 5
The moment of inertia about centroidal axis parallel to a side for a cube of mass m is
m a2/3
m a2/6
m a2/8
m a2/12
The moment of inertia of a uniform rod of mass m and length l about an axis through one end and perpendicular to the length of rod would be
m l2/3
m l2/6
m l2/8
m l2/12
The moment of inertia of a uniform rod of mass m and length l about an axis through its centre and perpendicular to the length of rod is
m l/6
m l2/12, m l/6
m l2/8
m l2/3
The radius of gyration of a circular area of radius r with respect to centroidal axis is
0.1 r
0.2 r
0.5 r
0.7 r
The ratio of moment of inertia of a circle and that of a square having same area about their centroidal axis is
The moment of inertia of a circular area of radius r with respect to diametral axis is______
The moment of inertia about diagonal of a square plate of side a is
a4/12
a4/6
a4/3
The ratio of the moment of inertia of a triangle of base width b and height h with respect to an axis coinciding with its base and a centroidal axis parallel to the base would be
2 : 1
3 : 1
1 : 4
6 : 1
The ratio of moment of inertia of a rectangle and that of a triangle, having same base and height, with respect to their bases would be
2 : 1
3 : 1
4 : 1
6 : 1
The moment of inertia of a triangle of base width b and height h with respect to an axis through the apex parallel to the base would be
bh3/4
bh3/8
bh3/12
bh3/36
A triangular plate in the form of an isosceles triangle ABC has base BC = 10 cm and altitude = 12 cm. From this plate, a portion in the shape of an isosceles triangle OBC is removed. If O is the mid point of the altitude of triangle ABC, then distance of CG of the reminder section from the base is
3.5 cm
4.8 cm
6 cm
8 cm
A right circular cone of 20 cm height weighs 1000 N. A cone of 8 cm height and 64 N weights is removed from the top. The distance of CG of the frustum from the base is approximately
2.5 cm
3.25 cm
4.25 cm
6 cm
If the distance between CG of two masses m1 and m2 is l, then the distance of CG of the composite system from mass m1 will be
Identify the wrong statement/statements.
Centre of mass of a body
must lie somewhere inside the body
is located at the geometric centre of the body
lies at the geometric centre of the body provided it is of uniform density
is synonymous with centre of gravity.
From a rectangular plate whose cross-section is 8 cm * 6 cm, circular disc of 3 cm2 in area is removed. If CG of the reminder is 1 mm from the CG of the rectangular plate, the distance of the centre of disc from the centre of rectangular plate is
1.0 cm
1.5 cm
2.5 cm
3 cm
The moment of inertia MOI of a body is
the moment of its inertia
the rotational analogue of mass
the rotational moment acting on the body
the inertial moment acting on the body
/
S m x
S m x2
S m x2 S m x
S m2 x S m
The MOI of a body does not depend upon
shape of the body
mass of the body and its distribution within the body
axis of rotation of the body
angular velocity of the body
Identify the incorrect statement/statements :
The area moment of inertia and the mass moment of inertia are two entirely unrelated concepts
An axis passing’s through the centroid and lying in the plane is called centroidal axis
Moment of inertia of a body equals twice the kinetic energy of rotation when angular velocity of the body is unity
Radius of gyration is the effective distance where the entire mass may be considered to be located with respect to the axis of rotation
None of the above
The moment of inertia of an area is always least with respect to
centroidal axis
vertical axis
radius of gyration
depends upon configuration of the area
The moment of inertia of rectangular element (b * h) about an axis coincident with side b would be
bh3/12
bh3/6
bh3/3
2bh3/3
For a rectangular element with sided b and h, the moment of inertia about its centroidal axis parallel to side b would be
bh3/3
bh3/12
bh3/24
bh3/36
The moment of inertia of a square of side A about an axis through its centre of gravity would be
A4/6
A4/12
A4/24
A4/36
The moment of inertia of a triangle of base width b and height h with respect to its base would be
bh3/8
bh3/12
bh3/24
bh3/36
The CG of a plane lamina will not be at its geometrical centre if it is a
circle
square
rectangle
right angled triangle
equilateral triangle.
The moment of inertia of a triangle of base b and altitude h with respect to a centroidal axis parallel to its base would be
bh3/12
bh3/18
bh3/24
bh3/36
The CG of a triangle lies at the point of intersection of
diagonals
altitudes
bisector of angles
medians
For a solid cone of height h, the CG lies on the axis at a distance above the base equal to
h/4
h/3
2h/3
3h/8
The position of CG of a solid hemisphere of radius r lies on the central radius at a distance (from the plane base)
2 r 3
3 r 4
3 r 8
1 r 2
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paper consists of 40 questions which are required to be finished in an hours time approximately.

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