The C.G. of a right circular cone lies on its axis of symmetry at a height of
h/2
h/3
h/4
h/5
Correct Answer :
C. h/4
Related Questions
Which of the following represents the state of neutral equilibrium?
A cube resting on one edge
A smooth cylinder lying on a curved surface
A smooth cylinder lying on a convex surface
None of the above
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
Power developed by a torque, is
2πNT kg m/min
2πNT/4500 h.p
2πNT /60 watts
All the above
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
The shape of a suspended cable for a uniformly distributed load over it is
Circular
Parabolic
Catenary
Cubic parabola
The reaction at the support D of the continuous beam ABCD, hinged at two points shown in below figure is 
1.6 t
1.6 t ↓
0.5 t
0.5 t ↓
Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m/sec and 1 m/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is
2/3
1/5
3/5
1/3
A ball moving with a velocity of 5 m/sec impinges a fixed plane at an angle of 45° and its direction after impact is equally inclined to the line of impact. If the coefficient of restitution is 0.5, the velocity of the ball after impact will be
0.5 m/sec
1.5 m/sec
2.5 m/sec
3.5 m/sec
The Law of Polygon of Forces states that
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
When a body of mass M1 is hanging freely and another of mass M2 lying on a smooth inclined plane(α) are connected by a light index tensile string passing over a smooth pulley, the acceleration of the body of mass M1, will be given by
g(M1 + M2 sin α)/(M1 + M2) m/sec
g(M1 - M2 sin α)/(M1 + M2) m/sec²
g(M2 + M1 sin α)/(M1 + M2) m/sec²
g(M2 × M1 sin α)/(M2 - M1) m/sec²
For a given velocity of a projectile, the range is maximum when the angle of projection is
30°
45°
90°
0°
If g1 and g2 are the gravitational accelerations on two mountains A and B respectively, the weight of a body when transported from A to B will be multiplied by
g1
g2
g1/g2
g2/g1
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
A smooth cylinder lying on its convex surface remains
In stable equilibrium
In unstable equilibrium
In neutral equilibrium
Out of equilibrium
A ball of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/sec hits an identical stationary ball B on the table. If the impact is perfectly plastic, the velocity of the ball B just after impact would be
Zero
5 m/sec
10 m/sec
None of these
A satellite moves in its orbit around the earth due to
Gravitational force
Centripetal force
Centrifugal force
None of these
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°
Power can be expressed as
Work/energy
Work/time
Work × time
Work/distance
Pick up the correct statement from the following:
Nature plays an important role in the launch of a satellite
The earth's gravity reduces the speed of a satellite by 32 km per second
The gravitational force relents as the satellite climbs higher
All the above
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
Lami's theorem states that
Three forces acting at a point are always in equilibrium
If three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium
Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
Three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
Pick up the incorrect statement from the following. In a simple harmonic motion
Velocity is maximum at its mean position
Velocity is minimum at the end of the stroke
Acceleration is minimum at the end of the stroke
Acceleration is zero at the mean position
If two forces acting at a point are in equilibrium, they must be equal in magnitude and their line of action must be along
The same line in the same sense
The same line in opposite sense
The perpendicular to both the lines
None of these
One half of a vibration of a body, is called
Period time
Oscillation
Beat
Amplitude
The ends of a string weighing w/metre are attached to two points at the same horizontal level. If the central dip is very small, the horizontal tension of the string throughout is
wl/4d
wl²/4d
wl²/8d
wl²/16d
A glass ball is shot to hit a wall from a point on a smooth floor. If the ball returns back to the point of projection in twice the time taken in reaching the wall, the coefficient of restitution between the glass ball and the wall is
0.25
0.33
0.40
0.50
A simple pendulum of length 1 has an energy E when its amplitude is A. If its amplitude is increased to 2 A, the energy becomes
E
E/2
2E
4E
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
A stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad/sec. The tension in the string is,
5 N
10 N
15 N
25 N
Newton's law of Collision of elastic bodies states that when two moving bodies collide each other, their velocity of separation
Is directly proportional to their velocity of approach
Is inversely proportional to their velocity of approach
Bears a constant ratio to their velocity of approach
Is equal to the sum of their velocities of approach