The moment of inertia of a circular lamina of diameter d, about an axis perpendicular to the plane of the lamina and passing through its centre, is
πd4/12
πd4/16
πd4/24
πd4/32
Correct Answer :
D. πd4/32
Related Questions
The condition of equilibrium for any system of forces in a plane is
That polygon of forces must close
That resultant couple must be zero
Both (A) and (B)
None of the above
A smooth cylinder lying on its convex surface remains
In stable equilibrium
In unstable equilibrium
In neutral equilibrium
Out of equilibrium
Two particles have been projected at angles 64° and 45° to the horizontal. If the velocity of projection of first is 10 m/sec, the velocity of projection of the other for equal horizontal ranges is
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7.3 m/sec
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Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis?
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Both discs will have same rotational inertia
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If G is the Gauge of track, v is velocity of the moving vehicle, g is the acceleration due to gravity and r is the radius of a circular path, the required super elevation is
gv²/Gr
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Vertical ordinate of the arch
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kg.m
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kg/sec2
kg/sec
Instantaneous center is at infinity when the angular velocity is
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Zero
Maximum
Minimum
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Tangentially at that point
Away from the centre
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If a projectile is fired with an initial velocity of 10 m/sec at an angle of 60° to the horizontal, its horizontal and vertical velocity at the highest point of trajectory are
0 and 5 m/sec
5 m/sec and 0
5√3 m/sec and 0
5 and 5√3 m/sec
When a body in equilibrium undergoes an infinitely small displacement, work imagined to be done, is known as
Imaginary work
Negative work
Virtual work
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The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is
1/4
1/2
3/4
2
The moment of inertia of a hollow circular section whose external diameter is 8 cm and internal diameter is 6 cm, about centroidal axis, is
437.5 cm4
337.5 cm4
237.5 cm4
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For a self-locking machine, the efficiency should be
Less than 60%
50 %
More than 50%
None of these
For a non-concurrent force system to be in equilibrium
Only the closure of force polygon is sufficient
Only the closure of funicular polygon is sufficient
Both force polygon and funicular polygon must close
None of the above
A block in the shape of a parallelepiped of sides 1m × 2m × 3m lies on the surface. Which of the faces gives maximum stable block?
1 m × 2 m
2 m × 3 m
1 m × 3 m
Equally stable on all faces
A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The efficiency of the lifting machine is
50 %
40 %
55 %
30 %
If the tension in a cable supporting a lift moving upwards is twice the tension when the lift is moving downwards, the acceleration of the lift, is
g/2
g/3
g/4
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When two forces, each equal to P, act at 90° to each other, then the resultant will be
P
P√2
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2P
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Uneven distribution of the gravitational field
Gravity of the sun and the moon
Aerodynamic forces
None of these
A train weighing 196 tonnes experiences a frictional resistance of 5 11/22 per tonne. The speed of the train at the top of a down gradient 1 in 78.4 is 36 km/hour. The speed of the train after running 1 km down the slope, is
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10 √5 m/sec
5 √3 m/sec
3 √5 m/sec
A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If r is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be
[r (π + 0.25)]/(π - 0.5)
[r (π - 0.5)]/(π + 0.25)
[r (π - 0.25)]/(π - 0.5)
[r (π + 0.25)]/(π + 0.5)
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Proportional to the square of the distance from the point of reference
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Inversely proportion to the distance from the point of reference
The gravitational force makes a satellite go round the earth in a circular orbit, if it is projected with an initial velocity of
8.04 km/sec at a height of 285 km
11.11 km/sec at a height of 37,400 km
11.26 km/sec, the satellite escapes the pull of the earth
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cm4
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gm.cm²
gm.cm3
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If a polygon representing the forces acting at point in a body is closed, the forces are in equilibrium
If forces acting on a point can be represented in magnitude and direction by the sides of a polygon taken in order, then the resultant of the forces will be represented in magnitude and direction by the closing side of the polygon
If forces acting on a point can be represented of a polygon taken in order, their sides of a polygon taken in order, their resultant will be represented in magnitude and direction by the closing side of the polygon, taken in opposite order
If forces acting on a point can be represented in magnitude and direction by the sides of a polygon in order, the forces are in equilibrium
A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first?
Sphere with greater rotational energy at bottom than cylinder
Sphere with lesser rotational energy at bottom than cylinder
Cylinder with greater rotational energy at bottom than sphere
Both reach the bottom simultaneously with equal rotational energy at bottom
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Straight line and parabola
Straight line and circle
Circle and straight line
Circle and parabola
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Circle
Equilateral triangle
Rectangle
Right angled triangle