Centre of gravity of a thin hollow cone lies on the axis of symmetry at a height of
One-half of the total height above base
One-third of the total height above base
One-fourth of the total height above base
None of these
Correct Answer :
B. One-third of the total height above base
Related Questions
A stone is whirled in a vertical circle, the tension in the string, is maximum
When the string is horizontal
When the stone is at the highest position
When the stone is at the lowest position
At all the positions
The force which produces an acceleration of 1 m/sec2 in a mass of one kg, is called
Dyne
Newton
Joule
Erg
M.I. of a thin ring (external diameter D, internal diameter d) about an axis perpendicular to the plane of the ring, is
π/64 (D4 + d4)
π/32 (D4 - d4)
π/32 (D4 + d4)
π/32 (D4 × d4)
Minimum potential energy of a system will be in the position of
Stable equilibrium
Unstable equilibrium
Neutral equilibrium
All of the above
A system of coplanar forces is in equilibrium when
Force polygon closes
Funicular polygon closes
Both force polygon and funicular polygon close
All the forces are concurrent
If two forces each equal to T in magnitude act at right angles, their effect may be neutralised by a third force acting along their bisector in opposite direction whose magnitude will be
2 T
1/2 T
√2 T
3 T
The centre of gravity of a triangle is at the point where three
Medians of the triangle meet
Perpendicular bisectors of the sides of the triangle meet
Bisectors of the angle of the triangle meet
None of these
If the resultant of two forces P and Q acting at an angle θ makes an angle α with P, then tan α equals
P sin θ/P - Q cos θ
Q sin θ/P + Q cos θ
P sin θ/P + Q tan θ
Q sin θ/P + Q sin θ
At a given instant ship A is travelling at 6 km/h due east and ship B is travelling at 8 km/h due north. The velocity of B relative to A is
7 km/hrs
2 km/hrs
1 km/hrs
10 km/hrs
Three forces which act on a rigid body to keep it in equilibrium. The forces must be coplanar and
Concurrent
Parallel
Concurrent parallel
None of these
The reaction RB of the roller support B of the beam shown in below figure is 
10.8 t
10.6 t
10.4 t
10.2 t
A square hole is made in a circular lamina, the diagonal of the square is equal to the radius of the circle as shown in below figure the shift in the centre of gravity is 
r (π - 0.75)/(π - 0.5)
r (π - 0.25)/(π - 0.75)
r (π - 0.5)/(π - 0.75)
r (π - 0.5)/(π - 0.25)
The direction of projection should bisect the angle between the inclined plane and the vertical for a range of a projectile on inclined plane
To be zero
To be maximum
To be minimum
None of these
A projectile is fired with a velocity of 100.3 m/sec. at an elevation of 60°. The velocity attained by the projectile when it is moving at a height of 100 m, is
70 m/sec
75 m/sec
80 m/sec
90 m/sec
The maximum value of the horizontal range for a projectile projected with a velocity of 98 m/sec is
98 m
490 m
980 m
1960 m
The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by
1 : 2
1 : 1
2 : 1
3 : 1
Two loads of 50 kg and 75 kg are hung at the ends of a rope passing over a smooth pulley shown in below figure. The tension in the string is: 
50 kg
75 kg
25 kg
60 kg
Force polygon method is applicable for
Any coplanar force system
A system of parallel forces only
Concurrent coplanar force system
Non-concurrent coplanar force system
The shape of a suspended cable for a uniformly distributed load over it is
Circular
Parabolic
Catenary
Cubic parabola
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 system of coplanar forces acting on a rigid body can be reduced to
One force only
One couple only
One force and one couple only
None of the above
Power can be expressed as
Work/energy
Work/time
Work × time
Work/distance
In simple harmonic motion, acceleration of a particle is proportional to
Rate of change of velocity
Displacement
Velocity
Direction
A body is said to move with Simple Harmonic Motion if its acceleration, is
Always directed away from the centre, the point of reference
Proportional to the square of the distance from the point of reference
Proportional to the distance from the point of reference and directed towards it
Inversely proportion to the distance from the point of reference
If the horizontal range is 2.5 times the greatest height, the angle of projection of the projectile, is
57°
58°
59°
60°
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
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 rigid body is in a stable equilibrium if the application of any force
Can raise the CG of the body but cannot lower it
Tends to lower the CG of the body
Neither raises nor lowers the CG of the body
None of above
If a spherical body is symmetrical about its perpendicular axes, the moment of inertia of the body about an axis passing through its centre of gravity as given by Routh's rule is obtained by dividing the product of the mass and the sum of the squares of two semi-axes by n. Where, n is
2
3
4
5
A stone is thrown up a slope of inclination 60° to the horizontal. At what angle to the slope must the stone be thrown so as to land as far as possible from the point of projection?
15°
30°
45°
75°