The velocity of a particle moving with simple harmonic motion, at any instant is given by (where ω = Displacement of the particle from mean position)
ω √(x² - r²)
ω √(r² - x²)
ω² √(x² - r²)
ω² √(r² - x²)
Correct Answer :
B. ω √(r² - x²)
Related Questions
The effort of a Porter governor is equal to (where c = Percentage increase in speed, m = Mass of ball, and M = Mass on the sleeve)
c (m - M) g
c (m + M) g
c/(m + M) g
c/(m - M) g
The coriolis component of acceleration depends upon
Velocity of slider
Angular velocity of the link
Both (A) and (B)
None of these
Which of the following would constitute a link?
Piston, piston rod and cross head
Piston and piston rod
Piston rod and cross head
Piston, crank pin and crank shaft
Which of the following governor is used to drive a gramophone?
Watt governor
Porter governor
Pickering governor
Hartnell governor
A reed type tachometer use the principle of
Longitudinal vibration
Torsional vibration
Transverse vibration
Damped free vibration
The two elements of a pair are said to form a higher pair, when they
Have a surface contact when in motion
Have a line or point contact when in motion
Are kept in contact by the action of external forces, when in motion
Permit relative motion
The frictional torque transmitted in a conical pivot bearing, considering uniform wear, is
(1/2) μ W R cosec α
(2/3) μ W R cosec α
(3/4) μ W R cosec α
μ W R cosec α
Ackermann steering gear consists of
Sliding pairs
Turning pairs
Rolling pairs
Higher pairs
The maximum fluctuation of energy is the
Difference between the maximum and minimum energies
Sum of the maximum and minimum energies
Variations of energy above and below the mean resisting torque line
Ratio of the mean resisting torque to the workdone per cycle
The cam and follower is an example of
Sliding pair
Rolling pair
Lower pair
Higher pair
Kinematic pairs are those which have
Point or line contact between the two elements when in motion
Surface contact between the two elements when in motion
Elements of pairs not held together mechanically
Two elements that permit relative motion
The driving and driven shafts connected by a Hooke's joint will have equal speeds, if
cosθ = sinα
sinθ = ± tanα
tanθ = ± cosα
cotθ = cosα
The mechanism consisting of three turning pairs and one sliding pair, is called a
Single slider crank chain
Whitworth quick return motion mechanism
Crank and slotted lever quick return motion mechanism
All of the above
When the crank is at the outer dead centre, in a reciprocating steam engine, then the acceleration of the piston will be
ω² r {(n + 1)/n}
ω² r {(n - 1)/n}
ω² r {n/(n + 1)}
ω² r {n/(n - 1)}
In order to facilitate starting of locomotive in any position, the cranks of a locomotive with two cylinders, are placed at
45° to each other
90° to each other
120° to each other
180° to each other
The Hooke's joint consists of:
Two forks
One fork
Three forks
Four forks
The following is the inversion of slider crank chain mechanism
Whitworth quick return mechanism
Hand pump
Oscillating cylinder engine
All of the above
If the rotating mass of a rim type flywheel is distributed on another rim type flywheel whose mean radius is half the mean radius of the former, then energy stored in the latter at the same speed will be
Four times the first one
Same as the first one
One fourth of the first one
One and a half times the first one
The frictional torque transmitted in a flat pivot bearing with assumption of uniform pressure is _________ as compared to uniform wear.
Less
More
Same
None of these
Module of a gear is
D/T
T/D
2D/T
2T/D
In a screw jack, the effort required to lift the load W is given by (where 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)
A flywheel is fitted to the crankshaft of an engine having W as the amount of indicated work per revolution and permissible limits of coefficient of fluctuation of energy and speed as CE and CS respectively. The kinetic energy of the flywheel is given by
2 W CE / CS
W CE / 2CS
W CE / CS
W CS / 2CE
If D₁ and D₂ be the diameters of driver and driven pulleys, then belt speed is proportional to
D₁/D₂
D₂/D₁
D₁.D₂
D₁
The natural frequency of free transverse vibrations due to uniformly distributed load acting over a simply supported shaft is (where δS = Static deflection of simply supported shaft due to uniformly distributed load)
0.4985/ √δS
0.5615/ √δS
0.571/ √δS
0.6253/ √δS
When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by (where r = Pitch circle radius of pinion, R = Pitch circle radius of wheel, and φ = Pressure angle)
[(r² + R²) cosφ]/2
[(r² + R²) sinφ]/2
[(r + R) cosφ]/2
[(r + R) sinφ]/2
In a screw jack, the effort required to lower the load W is given by
P = W tan(α - φ)
P = W tan(α + φ)
P = W tan(φ - α)
P = W cos(α + φ)
The relation between number of pairs (p) forming a kinematic chain and the number of links (l) is
l = 2p - 2
l = 2p - 3
l = 2p - 4
l = 2p - 5
The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)
m.ω².r sinθ
m.ω².r cosθ
m.ω².r (sin 2θ/n)
m.ω².r (cos 2θ/n)
The example of spherical pair is
Bolt and nut
Lead screw of a lathe
Ball and socket joint
Ball bearing and roller bearing
To transmit power from one rotating shaft to another whose axes are neither parallel nor intersecting, use?
Spur gear
Spiral gear
Bevel gear
Worm gear