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
Correct Answer :
A. 1/4
Related Questions
Principle of Transmissibility of Forces states that, when a force acts upon a body, its effect is
Maximum if it acts at the centre of gravity of the body
Different at different points on its line of
Same at every point on its line of action
Minimum if it acts at the C.G. of the body
Energy may be defined as
Power of doing work
Capacity of doing work
Rate of doing work
All the above
A flywheel of moment of inertia 20 kgm is acted upon by a tangential force of 5 N at 2 m from its axis, for 3 seconds. The increase in angular velocity in radian per second is
1/2
3/2
2
3
A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan1 x, where x is
3/4
4/5
5/3
3/5
Periodic time of body moving with simple harmonic motion, is
Directly proportional to its angular velocity
Directly proportional to the square of its angular velocity
Inversely proportional to the square of its angular velocity
Inversely proportional to its angular velocity
In case of S.H.M. the period of oscillation (T), is given by
T = 2ω/π²
T = 2π/ω
T = 2/ω
T = π/2ω
Time period and length of a seconds pendulum respectively are
1 sec and 99.4 cm
1 sec and 92.7 cm
2 sec and 99.4 cm
2 sec and 92.7 cm
The velocity of a moving body, is
A vector quantity
A scalar quantity
A constant quantity
None of these
The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is ½, the velocities of separation of the balls will be equal to
Original velocity in the same direction
Half the original velocity in the same direction
Half the original velocity in the opposite direction
Original velocity in the opposite direction
A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan1 x, where x is (Assume g = 10 m/sec²)
3/8
1/2
9/5
5/8
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
The centre of gravity of a trapezoidal dam section whose top width is a, bottom width is band the vertical side is a, from its vertical face is
(a² + ab + b²)/3 (a + b)
(b² + bc + c²)/3 (b + c)
(a² + ab + c²)/3 (a + c)
None of these
Pick up the correct statement from the following:
If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities
If a sphere impinges directly on an equal sphere which is at rest, then a fraction ½(1 - e2) the original kinetic energy is lost by the impact
If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles
All the above
The tension in a cable supporting a lift
Is more when the lift is moving downwards
Is less when the lift is moving upwards
Remains constant whether its moves downwards or upwards
Is less when the lift is moving downwards
The unit of impulse, is
kg.m/sec
kg.m/sec
kg.m/sec2
kg.m/sec
A smooth cylinder lying on its convex surface remains
In stable equilibrium
In unstable equilibrium
In neutral equilibrium
Out of equilibrium
Cartesian form of the equation of catenary is
y = c cosh x/c
y = c sinh x/c
y = c tan x/c
y = c sin x/c
If l is the span of a light suspension bridge whos each cable carries total weight (w) and the central dip is y, the horizontal pull at each support, is
wl/4y
wl/8y
wl/2y
wl
A Seconds pendulum executes
0.5 beat per second
1.0 beat per second
2.0 beats per second
2.5 beats per second
Which one of the following laws is not applicable to a simple pendulum?
The time period does not depend on its magnitude
The time period is proportional to its length l
The time period is proportional to l, where l is length
The time period is inversely proportional to g, where g is the acceleration due to gravity
A force P of 50 N and another force Q of unknown magnitude act at 90° to each other. They are balanced by a force of 130 N. The magnitude of Q is
60 N
80 N
100 N
120 N
If two forces of 3 kg and 4 kg act at right angles to each other, their resultant force will be equal to
7 kg
1 kg
5 kg
None of these
The C.G. of the shaded area of the below figure from the x-axis is 
a/4
3a/4
3b/10
3a/10
Parallelogram Law of Forces states, if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by
Its longer side
Its shorter side
The diagonal of the parallelogram which does not pass through the point of intersection of the forces
The diagonal of the parallelogram which passes through the point of intersection of the forces
Engineer's units of force, is
Newton in absolute units
Dyne in absolute units
Newton and dyne in absolute units
All the above
A string of length 90 cm is fastened to two points A and B at the same level 60 cm apart. A ring weighing 120 g is slided on the string. A horizontal force P is applied to the ring such that it is in equilibrium vertically below B. The value of P is:
40 g
60 g
80 g
100 g
The equation of motion of a particle starting from rest along a straight line is x = t3 - 3l2 + 5. The ratio of the velocities after 5 sec and 3 sec will be
2
3
4
5
The characteristic of a couple is:
Algebraic sum of forces, constituting a couple is zero
Algebraic sum of moments of forces, constituting a couple, about any point, is same
A couple can be never the balanced by a single force
All the above
A trolley wire weighs 1 kg per metre length. The ends of the wire are attached to two poles 20 m apart. If the horizontal tension is 1000 kg, the central dip of the cable is
2 cm
3 cm
4 cm
5 cm
The following statement is one of the laws of Dynamic friction
The force of friction always acts in a direction opposite to that in which a body is moving
The magnitude of the kinetic friction bears a constant ratio to the normal reaction between two surfaces. The ratio being slightly less than that in the case of limiting friction
For moderate speeds the force of friction remains constant but decreases slightly with the increase of speed
All the above