The C.G. of the shaded area of the below figure whose curve OM is a parabola from y-axis, is 
a/4
3a/4
3b/10
3a/10
Correct Answer :
B. 3a/4
Related Questions
For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is
α = π/4 - β/2
α = π/2 + β/2
α = β/2 - π/2
α = π/4 - β/2
The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then,
P = R
Q = R
P = Q
None of the above is correct
The shape of a suspended cable under its own weight, is
Parabolic
Circular
Catenary
Elliptical
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
A marble ball is rolled on a smooth floor of a room to hit a wall. If the time taken by the ball in returning to the point of projection is twice the time taken in reaching the wall, the coefficient of restitution between the ball and the wall, is
0.25
0.50
0.75
1.0
A number of forces acting simultaneously on a particle of a body
May not be replaced by a single force
May be replaced by a single force
May be replaced by a single force through C.G. of the body
May be replaced by a couple
A ball is dropped from a height of 2.25 m on a smooth floor and rises to a height of 1.00 m after the bounce. The coefficient of restitution between the ball and the floor is
0.33
0.44
0.57
0.67
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
The centre of gravity of a quadrant of a circle lies along its central radius at a distance of
0.2 R
0.4 R
0.3 R
0.6 R
The intrinsic equation of catenary is
S = c tan ψ
y = c cosh x/c
y = c cosh ψ
y = c sinh ψ
The centre of gravity of a plane lamina will not be at its geometrical centre if it is a
Circle
Equilateral triangle
Rectangle
Right angled triangle
The acceleration of a particle moving along the circumference of a circle with a uniform speed, is directed
Radially
Tangentially at that point
Away from the centre
Towards the centre
The frequency of oscillation on moon as compared to that on earth, will be
2.44 times more
2.44 times less
3 times less
3 times more
The reaction at the central support B of the beam ABC hinged at D shown in below figure is 
2 t
5.8 t
0.2 t
3.5 t
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
5 √10 m/sec
10 √5 m/sec
5 √3 m/sec
3 √5 m/sec
Two parallel forces 20 kg and 15 kg act. In order that the distance of the resultant from 20 kg force may be the same as that of the former resultant was from 15 kg, the 20 kg force is diminished by
5.5 kg
6.25 kg
8.75 kg
10.5 kg
Maximum efficiency of a screw jack for the angle of friction θ, is
sin θ/(1 + sin θ)
(1 - sin θ)/sin θ
(1 + sin θ)/(1 - sin θ)
(1 - sin θ)/(1 + sin θ)
The equation of motion of a particle starting from rest along a straight line is x = t3 - 3t2+ 5. The ratio of the accelerations after 5 sec and 3 sec will be
2
3
4
5
The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be
30°
45°
60°
75°
Which of the following is a scalar quantity?
Energy
Momentum
Torque
Impulse
The rotational velocity of a satellite is increased by 450 m per second if its launch is done from equator
Eastward
Northward
Westward
Southward
From a solid cylinder of height 8 cm and radius 4 cm, a right circular cone is scooped out on the same base and having the same height as that of the cylinder. The C.G. of the remainder is at a height of
4.5 cm
5.0 cm
5.25 cm
5.5 cm
Free body diagram is an
Isolated joint with only body forces acting on it
Isolated joint with internal forces acting on it
Isolated joint with all the forces, internal as well as external, acting on it
None of the above
A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
Floor is smooth and wall is rough
Floor is rough and wall is smooth
Both floor and wall are rough
Both floor and wall are smooth
If α is the angular acceleration of a compound pendulum whose angular displacement is θ, the frequency of the motion is
2π √(α/θ)
(1/2π) √(α/θ)
4π √(α/θ)
2π √(α - θ)
A sphere is resting on two planes BA and BC which are inclined at 45° and 60° respectively with the horizontal. The reaction on the plane BA will be
Less than that on BC
More than that of BC
Equal to that on BC
None of these
The maximum velocity of a body vibrating with a simple harmonic motion of amplitude 150 mm and frequency 2 vibrations/sec, is
188.5 m/sec
18.85 m/sec
1.885 m/sec
0.18845 m/sec
A body A of mass 6.6 kg which is lying on a horizontal platform 4.5 m from its edge is connected to the end of a light string whose other end is supporting a body of mass 3.2 kg as shown in below figure. If the friction between the platform and the body A is 1/3, the acceleration is 
0.5 m/sec2
0.75 m/sec2
1.00 m/sec2
1.25 m/sec2
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
137.5 cm4
From a circular plate of a diameter 6 cm is cut out a circle whose diameter is equal to the radius of the plate. The C.G. of the remainder from the centre of circular plate is at a distance of
2.0 cm
1.5 cm
1.0 cm
0.5 cm