The centre of gravity of an isosceles triangle with base (p) and sides (q) from its base is
[√(4p² - q²)]/6
(4p² - q²)/6
(p² - q²)/4
(p² + q²)/4
Correct Answer :
A. [√(4p² - q²)]/6
Related Questions
According to the law of moments, if a number of coplanar forces acting on a particle are in equilibrium, then
Their algebraic sum is zero
Their lines of action are at equal distances
The algebraic sum of their moments about any point in their plane is zero
The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point.
The Cartesian equation of trajectory is (where u = Velocity of projection, α = Angle of projection, and x, y = Co-ordinates of any point on the trajectory after t seconds.)
y = (gx²/2u² cos²α) + x. tanα
y = (gx²/2u² cos²α) - x. tanα
y = x. tanα - (gx²/2u² cos²α)
y = x. tanα + (gx²/2u² cos²α)
The total motion possessed by a body, is called
Impulsive force
Mass
Weight
Momentum
According to Newton's first law of motion,
Everybody continues in its state of rest or of uniform motion, in a straight line, unless it is acted upon by some external force
The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts
To every action, there is always an equal and opposite reaction
None of the above
One joule is equal to
0.1 N-m
1 N-m
10 N-m
100 N-m
A couple produces
Translatory motion
Rotational motion
Combined translatory and rotational motion
None of the above
Joule is the unit of
Force
Work
Power
Velocity
Coplanar concurrent forces are those forces which
Meet at one point, but their lines of action do not lie on the same plane
Do not meet at one point and their lines of action do not lie on the same plane
Meet at one point and their lines of action also lie on the same plane
Do not meet at one point, but their lines of action lie on the same plane
When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as
Simple pendulum
Compound pendulum
Torsional pendulum
Second's pendulum
On the ladder resting on the ground and leaning against a smooth vertical wall, the force of friction will be
Downwards at its upper end
Upwards at its upper end
Perpendicular to the wall at its upper end
Zero at its upper end
The equivalent length of a simple pendulum which gives the same frequency as compound pendulum is
h/(kG² + h²)
(kG² + h²)/h
h²/(kG² + h²)
(kG² + h²)/h²
Effect of a force on a body depends upon
Magnitude
Direction
Position or line of action
All of the above
The bodies which rebound after impact are called
Inelastic bodies
Elastic bodies
Neither elastic nor inelastic bodies
None of these
The coefficient of friction depends on
Area of contact
Shape of surfaces
Strength of surfaces
Nature of surface
Centre of gravity of a solid cone lies on the axis at the height
One fourth of the total height above base
One third of the total height above base
One-half of the total height above base
Three eighth of the total height above the base
The velocity ratio of a first system of pulleys with 4 pulleys is
4
8
16
20
The centre of percussion of the homogeneous rod of length L suspended at the top will be
L/2
L/3
3L/4
2L/3
The periodic time of one oscillation for a simple pendulum is (where l = Length of the pendulum.)
(1/2π). √(l/g)
(1/2π). √(g/l)
2π. √(l/g)
None of these
A weight of 1000 N can be lifted by an effort of 80 N. If the velocity ratio is 20, the machine is
Reversible
Non-reversible
Ideal
None of these
One end of a helical spring is fixed while the other end carries the load W which moves with simple harmonic motion. The frequency of motion is given by (where δ = Deflection of the spring.)
2π. √(g/δ)
1/2π. √(g/δ)
2π. √(δ/g)
1/2π. √(δ/g)
Which of the following is not the unit of pressure?
kg/cm
Bar
Atmosphere
Newton
In the equation of virtual work, following force is neglected
Reaction of any smooth surface with which the body is in contact
Reaction of a rough surface of a body which rolls on it without slipping
Reaction at a point or an axis, fixed in space, around which a body is constrained to turn
All of the above
If P is the force acting on the body, m is the mass of the body and a is the acceleration of the body, then according to Newton's second law of motion,
P + m.a = 0
P - m.a = 0
P × m.a = 0
P/m.a = 0
In a screw jack, the effort required to lift the load is given by (where W = Load lifted, α = Helix angle, and φ = Angle of friction.)
P = W tan (α - φ)
P = W tan (α + φ)
P = W tan (φ - α)
P = W cos (α + φ)
In the shown figure, if the angle of inclination of the plane is increased, then acceleration of the system will 
Increase
Decrease
Remain the same
None of these
The centre of percussion is below the centre of gravity of the body and is at a distance equal to
h/kG
h2/kG
kG2/h
h × kG
The unit of force in S.I. system of units is
Dyne
Kilogram
Newton
Watt
The friction experienced by a body, when at rest, is known as
Static friction
Dynamic friction
Limiting friction
Coefficient of friction
The energy possessed by a body, for doing work by virtue of its position, is called
Potential energy
Kinetic energy
Electrical energy
Chemical energy
The static friction
Bears a constant ratio to the normal reaction between the two surfaces
Is independent of the area of contact, between the two surfaces
Always acts in a direction, opposite to that in which the body tends to move
All of the above