In a simple harmonic motion, the position of equilibrium is always
Stable
Unstable
Neutral
None of the above
Correct Answer :
A. Stable
Related Questions
The motion of a particle is described by the relation x = t2- 10t + 30, where x is in metres and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be
Zero
30 m
50 m
60 m
A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If r is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be
[r (π + 0.25)]/(π - 0.5)
[r (π - 0.5)]/(π + 0.25)
[r (π - 0.25)]/(π - 0.5)
[r (π + 0.25)]/(π + 0.5)
One end of an elastic string of natural length / and modulus X is kept fixed while to the other end is attached a particle of mass m which is hanging freely under gravity. The particle is pulled down vertically through a distance x, held at rest and then released. The motion is
A simple harmonic motion
A rectilinear motion with constant speed
A damped oscillatory motion
None of the above
Select the correct statement
The body centrode rolls on the space centrode
The space centrode rolls on the body centrode
Both body and space centrodes may role on each other
The body centrode never touches space centrode
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
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°
If the angle between the applied force and the direction of motion of a body, is between 90° and 180°, the work done, is called
Virtual work
Imaginary work
Zero work
Negative work
The unit of Moment of Inertia of a body, is
m
m2
m3
m4
A bullet weighing 200 g is fired horizontally with a velocity of 25 m/sec from a gun carried on a carriage which together with the gun weighs 100 kg. The velocity of recoil of the gun, will be
0.01 m/sec
0.05 m/sec
1.00 m/sec
1.5 m/see
The C.G. of a thin hollow cone of height h, above its base lies on the axis, at a height of
h/3
h/4
2h/3
3h/4
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°
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 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 time period of a simple pendulum depends on (i) Mass of suspended particle (ii) Length of the pendulum (iii) Acceleration due to gravity The correct answer is
Only (i)
Both (ii) and (iii)
Both (i) and (iii)
All are correct
A block of weight 50 kg is placed on a horizontal plane. When a horizontal force of 18 kg is applied, the block is just on the point of motion. The angle of friction is
17° 48'
18° 48'
19° 48'
20° 48'
The vertical reaction at the support A of the structure shown in below figure, is 
1 t
2 t
3 t
3.5 t
The motion of a particle moving with S.H.M. from an extremity to the other, constitutes
Half an oscillation
One full oscillation
Two oscillations
None of these
A cube on a smooth horizontal surface
Cannot be in stable equilibrium
Cannot be in neutral equilibrium
Cannot be in unstable equilibrium
Can be in any of these states
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
According to Kennedy's theorem, if three bodies have plane motions, their instantaneous centres lie on
A point
A straight line
Two straight lines
A triangle
The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is
Less than 1
Equal to 1
Between 1 and 2
Greater than 2
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
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
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)
From the circular plate of a diameter 6 cm is cut out a circular plate whose diameter is equal to radius of the plate. The C.G. of the remainder shifts from the original position through
0.25 cm
0.50 cm
0.75 cm
1.00 cm
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
Time required to stop a car moving with a velocity 20 m/sec within a distance of 40 m, is
2 sec
3 sec
4 sec
5 sec
Moment of inertia of a squares of side b about an axis through its centre of gravity, is
b3/4
b4/12
b4/3
b4/8
If the angular distance, 0 = 2t3 - 3t², the angular acceleration at t = 1 sec. is
1 rad/sec²
4 rad/sec²
6 rad/sec²
12 rad/sec²
The displacement of a particle which moves along a straight line is given by S = 4t3 + 3t2- 10 where S is in meters and t is in seconds. The time taken by the particle to acquire a velocity of 18 m/sec from rest, is
½ sec
1 sec
1.2 sec
1.5 sec