A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is
1.00 m/sec
1.57 m/sec
3.14 m/sec
6.28 m/sec
Correct Answer :
C. 3.14 m/sec
Related Questions
Periodic time of a particle moving with simple harmonic motion is the time taken by the particle for
Half oscillation
Quarter oscillation
Complete oscillation
None of these
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
At the instantaneous center, the velocity of the moving lamina at any instant is
Zero
Maximum
Minimum
Varying
A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The velocity ratio of the lifting machine is
50
55
60
65
One Joule is equivalent to
9.81 Newton metre
1 Newton metre
1 kg wt metre
1 dyne metre
A disc of mass 4 kg, radius 0.5 m and moment of inertia 3 kgm² rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is
50 J
150 J
200 J
400 J
The resultant of two forces acting at right angles is 5 kgf and if they act at an angle of 60°, it is 37 kgf. The magnitudes of the forces are:
2 kgf, 3 kgf
3 kgf, 4 kgf
4 kgf, 5 kgf
5 kgf, 3 kgf
Rate of change of angular momentum is equal to
Force
Torque
Linear momentum
Impulse
Two forces act an angle of 120°. If the greater force is 50 kg and their resultant is perpendicular to the smaller force, the smaller force is
20 kg
25 kg
30 kg
35 kg
A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The efficiency of the lifting machine is
50 %
40 %
55 %
30 %
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
A block in the shape of a parallelepiped of sides 1m × 2m × 3m lies on the surface. Which of the faces gives maximum stable block?
1 m × 2 m
2 m × 3 m
1 m × 3 m
Equally stable on all faces
If G is the Gauge of track, v is velocity of the moving vehicle, g is the acceleration due to gravity and r is the radius of a circular path, the required super elevation is
gv²/Gr
Gr²/gr
Gr²/gv²
Gv²/gv
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
In a simple screw jack, the pitch of the screw is 9 mm and length of the handle operating the screw is 45 cm. The velocity ratio of the system is
1.5
5
25
314
The resultant of two forces P and Q acting at an angle θ, is
P2 + Q2 + 2P sin θ
P2 + Q2 + 2PQ cos θ
P2 + Q2 + 2PQ tan θ
√(P2 + Q2 + 2PQ cos θ)
The equation of motion of a particle starting from rest along a straight line is x = t3 - 3l2 + 5. The ratio of the velocities after 5 sec and 3 sec will be
2
3
4
5
The bending moment in an arch is proportional to
Vertical ordinate of funicular polygon
Vertical ordinate of the arch
Intercept between the arch axis and the funicular polygon
None of these
A cable loaded with 0.5 tonne per horizontal metre span is stretched between supports in the same horizontal line 400 m apart. If central dip is 20 m, the minimum tension in the cable, will be
200 tonnes at the centre
500 tonnes at the centre
200 tonnes at the right support
200 tonnes at the left support
The member forces in a statically in determinate truss
Can be obtained by graphic statics
Cannot be obtained by graphic statics
May be obtained by graphic statics
Can be obtained by graphic statics by trial and error
Which of the following is a scalar quantity?
Energy
Momentum
Torque
Impulse
A particle moving with a simple harmonic motion, attains its maximum velocity when it passes
The extreme point of the oscillation
Through the mean position
Through a point at half amplitude
None of these
For a non-concurrent force system to be in equilibrium
Only the closure of force polygon is sufficient
Only the closure of funicular polygon is sufficient
Both force polygon and funicular polygon must close
None of the above
Total no of instantaneous centres of a machine having n links, is
n/2
n
(n - 1)
n (n - 1)/2
The unit of Moment of Inertia of a body, is
m
m2
m3
m4
The angle of projection at which the horizontal range and maximum height of a projectile are equal to
36°
45°
56°
76°
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
If the angle of projection is double the angle of inclination (α) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be
½ cos α
½ sin α
½ tan α
2 cos α
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 maximum frictional force which comes into play, when a body just begins to slide over the surface of a another body, is known
Sliding friction
Rolling friction
Limiting friction
None of these