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engineering
machine elements in mechanical design

Theory Of Machines Kinematics And Dynamics 3rd Edition Sadhu Singh - Solutions

In which of the following case, the turning moment diagram will have least variations:(a) Double acting steam engine(b) Four stroke single cylinder petrol engine(c) 8 cylinder, 4 stroke diesel engine(d) Pelton wheel.
Which of the following statement is correct:1). If a rotor is statically balanced it is always dynamically balanced also 2). If a rotor is dynamically balanced, it must be statically balanced 3). If a rotor is dynamically balanced, it may or may not be statically balanced 4). If a rotor is
Which of the following are inversions of a double slider crank chain?1). Whitworth return motion 2). Scotch Yoke 3). Oldham's Coupling 4). Rotary engine Select correct answer using the codes given below: Codes:(a) 1 and 2(b) 1,3 , and 4(c) 2 and 3(d) 2,3 , and 4 .
Consider the following statements:Coriolis component of acceleration depends on 1). velocity of slider 2). angular velocity of the link 3). acceleration of slider 4). angular acceleration of link Of these statements(a) 1 and 2 are correct(b) 1 and 3 are correct(c) 2 and 4 are correct(d) 1 and 4 are
\(A B C D\) is a four-bar mechanism in which \(A B=30 \mathrm{~cm}\) and \(C D=45 \mathrm{~cm} . A B\) and \(C D\) are both perpendicular to fixed link \(A D\), as shown in the Fig.1. If velocity of \(B\) at this conditions is \(V\), then velocity of \(\mathrm{C}\) is(a) \(V\)(b) \(3 / 2 V\)(c) \(9
Consider the following follower motions in respect of a given lift, speed of rotation and angle of stroke of a cam:1). Cycloidal motion 2). Simple harmonic motion 3). Uniform velocity motion Which one of the following is the correct sequence of the above in the descending order of maximum
If \(\alpha=\) helix angle, and \(p_{c}=\) circular pitch; then which one of the following correctly expresses the axial pitch of a helical gear?(a) \(p_{c} \cos \alpha\)(b) \(\frac{p_{c}}{\cos \alpha}\)(c) \(\frac{p_{c}}{\tan \alpha}\)(d) \(p_{c} \sin \alpha\).
In a slider-bar mechanism, when does the connecting rod have zero angular velocity?(a) When crank angle \(=0^{\circ}\)(b) When crank angle \(=90^{\circ}\)(c) When crank angle \(=45^{\circ}\)(d) Never.
The turning moment diagram for a single cylinder double acting steam engine consists of +ve and -ve loops above and below the average torque line. For the +ve loop, the ratio of the speeds of the flywheel at the beginning and the end is which one of the following?(a) Less than unity(b) Equal to
Which one of the following is the correct statement?In meshing gears with involute gear teeth, the contact begins at the intersection of the(a) line of action and the addendum circle of the driven gear(b) line of action and the pitch circle of the driven gear(c) dedendum circle of the driver gear
Interference between the teeth of two meshing involute gears can be reduced or eliminated by 1). Increasing the addendum of the gear teeth and correspondingly reducing the addendum of the pinion 2). Reducing the pressure angle of the teeth of the meshing gears 3). Increasing the centre distance
What is the direction of the Coriolis components of acceleration in a slotted lever-crank mechanism?(a) Along the sliding velocity vector(b) Along the direction of the crank(c) Along a line rotated \(90^{\circ}\) from the sliding velocity vector in a direction opposite to the angular velocity of
The controlling force curves for a spring-controlled governor are shown in the below Fig.69. Which curve represents a stable governor?(a) 1 (b) 2 (c) 3 (d) 4. Controlling force Radius rotation Fig.69 3 4
For a governor running at constant speed, what is the value of the force acting on the sleeve?(a) Zero(b) Variable depending upon the load(c) Maximum(d) Minimum.
What is the condition for dynamic balancing of a shaft-rotor system?(a) \(\Sigma M=0\) and \(\Sigma F=0\)(b) \(\Sigma M=0\)(c) \(\Sigma F=0\)(d) \(\Sigma M+\Sigma F=0\).
For a three-cylinder radial engine, the primary and direct reverse cranks are as shown in the below Fig. 70.\((\mathrm{W}=\) Weight of reciprocating parts per cylinder).Which one of the following pairs is not correctly matched in this regard?(a) Primary direct force \(\ldots \frac{3 W}{2 g}
A uniform bar, fixed at one end carries a heavy concentrated mass at the other end. The system is executing longitudinal vibrations. The inertia of the bar may be taken into account by which one of the following portions of the mass of the bar at the free end?(a) \(\frac{5}{384}\)(b)
A motion is aperiodic at what value of the damping factor?(a) 1.0 or above(b) 0.5(c) 0.3(d) 0.866 .
A rolling disc of radius ' \(r\) ' and mass ' \(m\) ' is connected to one end of a linear spring of stiffness ' \(k\) ', as shown in the below Fig.71. The natural frequency of oscillation is given by which one of the following?(a) \(\omega=\sqrt{\frac{2}{3} \frac{k}{m}}\)(b)
In a \(6 \times 20\) wire rope, number 6 indicates the(a) diameter of the wire rope in \(\mathrm{mm}\)(b) number of strands in the wire rope(c) number of wires(d) gauge number of the wire.
Which one of the following statements relating to belt drives is correct?(a) The rotational speeds of the pulleys are directly proportional to their diameters(b) The length of the crossed belt increases as the sum of the diameters of the pulleys increases(c) The crowing of the pulleys is done to
A force ' \(F\) ' is to be transmitted through a square threaded power screw into a nut. If ' \(t\) ' is the height of the nut and ' \(d\) ' is the minor diameter, then which one of the following is the average shear stress over the screw thread?(a) \(\frac{2 F}{\pi \mathrm{d} t}\)(b)
In the compound gear train shown in the below Fig.72, gears \(A\) and \(C\) have equal numbers of teeth and gears \(B\) and \(D\) have equal numbers of teeth. When \(A\) rotates at \(800 \mathrm{rpm}, D\) rotates at \(200 \mathrm{rpm}\). The rotational speed of compound gears \(B C\) would then
Under service conditions involving jurking, vibration and pulsation of the working load, the bolt of choice would be a(a) short bolt with high rigidity(b) long bolt with increased elasticity(c) bolt with a dished washer(d) bolt with castle nut.
Gearing contact is which one of the following?(a) Sliding contact(b) Sliding contact, only rolling at pitch point(c) Rolling contact(d) Rolling and sliding at each point of contact.
Maximum angular velocity of the connecting rod with a crank to connecting rod ratio 1:5 for crank speed of \(3000 \mathrm{rpm}\) is around:(a) \(300 \mathrm{rad} / \mathrm{s}\)(b) \(60 \mathrm{rad} / \mathrm{s}\)(c) \(30 \mathrm{rad} / \mathrm{s}\)(d) \(3000 \mathrm{rad} / \mathrm{s}\).
Consider the following statements:1). One way of improving vibration isolation is to decrease the mass of the vibrating object 2). For effective isolation, the natural frequency of the system should be far less than the exciting frequency Which of the statements given above is/are correct?(a) 1
Common contact ratio of a pair of spur pinion and gear is(a) less than 1.0(b) equal to 1(c) between 2 and 3(d) greater than 3 .
In case of a multiple disc clutch, if \(n_{1}\) is the number of discs on the driving shaft and \(n_{2}\) is the number of discs on the driven shaft, then what is the number of pairs of contact surfaces?(a) \(n_{1}+n_{2}\)(b) \(n_{1}+n_{2}-1\)(c) \(n_{1}+n_{2}+1\)(d) \(n_{1}+2 n_{2}\).
For roller chain drive with sprocket having 10 teeth, the velocity of the driven shaft with respect to that of drive will be approximately(a) same(b) \(5 \%\) above(c) \(5 \%\) below(d) \(5 \%\) above to \(5 \%\) below.
Which of the following in-line engines working on four-stroke cycle is completely balanced inherently?(a) 2 cylinder engine(b) 3 cylinder engine(c) 4 cylinder engine(d) 6 cylinder engine.
Match List I with List II and select the correct answer using the code given below the lists: List I (Principle/method) A. Klein's construction B. Kennedy's theorem C. D'Alembert's principle D. Grubler's rule Codes: (a) (b) (c) (d) A C 12424 B1331 14242 D 3 1 1 3 List II (Corresponding Application)
Which mechanism produces intermittent rotary motion from continuous rotary motion?(a) Whitworth mechanism(b) Scotch Yoke mechanism(c) Geneva mechanism(d) Elliptical trammel.
The Fig. 73 below shows the schematic of an automobile having a mass of \(900 \mathrm{~kg}\) and the suspension spring constant of \(81 \times 40^{4} \mathrm{~N} / \mathrm{m}\). If it travels at a speed of \(72 \mathrm{~km} / \mathrm{hr}\) on a rough road with periodic waviness as shown, what is
Which one of the following mechanisms represents an inversion of the single slider crank chain?(a) Elliptical trammel(b) Oldham's coupling(c) Whitworth quick return mechanism(d) Pantograph mechanism.
At a given instant, a disc is spinning with angular velocity \(\omega\) in a plane at right angles to the paper (see the Fig.74) and after a short interval of time \(\delta\) t, it is spinning with angular velocity \(\omega+\) \(\delta \omega\) and the axis of spin has changed direction by the
The given Fig. 75 shows a slider crank mechanism in which link 1 is fixed. The number of instantaneous centres would be(a) 4 (b) 5 (c) 6 (d) 12 . 3 2 4 Fig.75 1
Consider the following statements:The Klein's construction for slider crank mechanism with crank rotating at constant angular velocity provides values of 1). piston velocity 2). piston acceleration 3). normal acceleration of crank pin Of these statements(a) 1 and 2 are correct(b) 1, 2, 3, and 4 are
If two parallel shafts are to be connected and the distance between the axes of shafts is small and variable, then one would need to use(a) a clutch(b) a universal joint(c) an Oldham's coupling(d) a knuckle joint
Consider the following statements relating to the curve for the inertia torque \(v / s\) crank angle for a horizontal, single cylinder petrol engine shown in the given Fig.76:1). \(\theta_{1}+\theta_{2}=180^{\circ}\)2). \(T_{1}=T_{2}\)3). \(\theta_{1} eq \theta_{2}\)4). \(A_{1}=A_{2}\)Of these
The height \(h\) of Porter governor with equal arms pivoted at equal distance from axis of rotation is expressed as (where \(m=\) mass of balls of the governor, \(M=\) mass of sleeve of the governor and \(N=\mathrm{rpm})\)(a) \(h=91.2\left[\frac{m+M}{m}\right] \frac{g}{N^{2}}\)(b)
Match List I (Type of Governor) with List II (Characteristics) and select the correct answer using the codes given below the lists: List I A. Isochronous governor B. Sensitive governor C. Hunting governor D. Stable governor List II 1. Continuously fluctuates above and below mean speed 2. For each
Consider the following statements:An in-line four-cylinder four-stroke engine is completely balanced for 1). primary forces 2). secondary forces 3). primary couples 4). secondary couples Of these statements(a) 1,3 , and 4 are correct(b) 1,2, and 4 are correct(c) 1 and 3 are correct(d) 2 and 4 are
A uniform cantilever beam undergoes transverse vibrations. The number of natural frequencies associated with the beam is(a) 1(b) 10(c) 100(d) infinite.
Two vibratory systems are shown in the given Fig.77 (1 and 2). The ratio of the natural frequency of longitudinal vibration of the second system to that of the first is(a) 4 (b) 2 (c) 0.5 (d) 0.25 . TTTTTT TTTTTT .4k m (1) Fig.77 m (2)
A shaft, supported on two bearings at its ends, carries two flywheels ' \(L\) ' apart. Mass moment of inertia of the two flywheels are \(I_{a}\) and \(I_{b}\), I being the polar moment of inertia of cross-sectional area of the shaft. Distance \(l_{a}\) of the mode of torsional vibration of the
A rack is a gear of(a) infinite diameter(b) infinite module(c) zero pressure angle(d) large pitch.
The maximum efficiency for spiral gears in mesh is given by (where \(\theta=\) shaft angle and \(\phi=\) friction angle)(a) \(\frac{1+\cos (\theta-\phi)}{1+\cos (\theta+\phi)}\)(b) \(\frac{1+\cos (\theta+\phi)}{1+\cos (\theta-\phi)}\)(c) \(\frac{1-\cos (\theta-\phi)}{1+\cos (\theta+\phi)}\)(d)
The block diagram of an automatic control system is shown in the following Fig. 78. Its simplified form will be as in (a) R GG2 C 1+GH (c) R G-G + 1+GH H Fig.78 (b) R G2-G C 1+GH (d) R G+G2 C 1+GH
Consider the following statements in respect of a body executing simple harmonic motion:1). Periodic time is the time for one complete revolution 2). The acceleration is directed towards the centre of suspension 3). The acceleration is proportional to distance from mean position 4). The velocity
A four-bar mechanism \(A B C D\) is shown in the given Fig.79. If the linear velocity ' \(V_{B}\) ' of the point ' \(B\) ' is \(0.5 \mathrm{~m} / \mathrm{s}\), then the linear velocity ' \(V\) ' of point ' \(C\) ' will be(a) \(1.25 \mathrm{~m} / \mathrm{s}\)(b) \(0.5 \mathrm{~m} / \mathrm{s}\)(c)
If reduction ratio of about 50 is required in a gear drive, then the most appropriate gearing would be(a) spur gears(b) bevel gears(c) double helical gears(d) worm and worm wheel.
A spring of stiffness ' \(k\) ' extended from a displacement \(x_{1}\) to a displacement \(x_{2}\). The work done by the spring is(a) \(\frac{1}{2} k x_{1}^{2}-\frac{1}{2} k x_{2}^{2}\)(b) \(\frac{1}{2} k\left(x_{1}-x_{2}\right)^{2}\)(c) \(\frac{1}{2} k\left(x_{1}+x_{2}\right)^{2}\)(d)
In a reciprocating engine mechanism, the crank and connecting rod of same length \(r\) metres are at right angles to each-other at a given instant, when the crank makes an angle of \(45^{\circ}\) with IDC. If the crank rotates with a uniform velocity of \(\omega \mathrm{rad} / \mathrm{s}\), the
A simplified turning moment diagram of a four-stroke engine is shown in the given Fig.80. If the mean torque ' \(T_{m}\) ' is \(10 \mathrm{Nm}\), the estimated peak torque ' \(T_{p}\) ' will be (assuming negative torque demand is negligible)(a) \(80 \mathrm{Nm}\)(b) \(120 \mathrm{Nm}\)(c) \(60
The height of a simple Watt governor running at a speed ' \(\mathrm{N}\) ' is proportional to(a) \(\mathrm{N}\)(b) \(\frac{1}{\mathrm{~N}}\)(c) \(\mathrm{N}^{2}\)(d) \(\frac{1}{\mathrm{~N}^{2}}\).
The controlling force curve of spring-loaded governor is given by the equation \(F=a r-c\), (where \(r\) is the radius of rotation of the governor balls and \(a, c\) are constants). The governor is(a) stable(b) unstable(c) isochronous(d) insensitive.
Two rotors are mounted on a shaft. If the unbalanced force due to one rotor is equal in magnitude to the unbalanced force due to the other rotor, but positioned exactly \(180^{\circ}\) apart, then the system will be balanced(a) statically(b) dynamically(c) statically as well as dynamically(d)
The primary direct crank of a reciprocating engine is located at an angle \(\theta\) clockwise. The secondary direct crank will be located at an angle(a) \(2 \theta\) clockwise(b) \(2 \theta\) anti-clockwise(c) \(\theta\) clock-wise(d) \(\theta\) anticlockwise.
The given Fig. 81 shows vibrations of a mass ' \(M\) ' isolated by means of springs and a damper. If an external force ' \(F\) ' \((=A \sin \omega \mathrm{t})\) acts on the mass and the damper is not used, then(a) \(\omega=\sqrt{\frac{k}{M}}\)(b) \(\omega=\frac{1}{2} \sqrt{\frac{k}{M}}\)(c)
The transmitted force through a mass-spring damper system will be greater than that transmitted through rigid supports for all values of damping factors, if the frequency ratio \(\left(\frac{\omega}{\omega_{n}}\right)\) is(a) more than \(\sqrt{2}\)(b) less than \(\sqrt{2}\)(c) equal to one(d) less
In a forced vibrations with viscous damping, maximum amplitude occurs when the forced frequency is(a) equal to natural frequency(b) slightly less than natural frequency(c) slightly greater than natural frequency(d) zero.
The rotor of a turbine is generally rotated at(a) the critical speed(b) a speed much below the critical speed(c) a speed much above the critical speed(d) a speed having no relation to critical speed.
The characteristic equation of a closed-loop automatic control system in time domain is given by\[ D^{5}+2 D^{4}+4 D^{2}+D+1=0 \]Consider the following statements in this regard:1). The system is linear 2). The system is non-linear 3). The system is stable 4). The system is unstable Of these
The given Fig. 82 shows a/an(a) locked chain (b) constrained kinematic chain (c) unconstrained kinematic chain (d) mechanism. Fig.82
In a four-link kinematic chain, the relation between the number of links \((L)\) and number of pairs \((J)\) is(a) \(L=2 J+4\)(b) \(L=2 J-4\)(C) \(L=4 J+2\)(d) \(L=4 J-2\).
An imaginary circle which by pure rolling action, gives the same motion as the actual gear, is called(a) addendum circle(b) pitch circle(c) dedendum circle(d) base circle.
The pressure angle of a spur gear normally varies from(a) \(14^{\circ}\) to \(20^{\circ}\)(b) \(20^{\circ}\) to \(25^{\circ}\)(c) \(30^{\circ}\) to \(36^{\circ}\)(d) \(40^{\circ}\) to \(50^{\circ}\).
If the number of teeth on the wheel rotating at \(300 \mathrm{rpm}\) is 90 , then the number of teeth on the mating pinion rotating at \(1500 \mathrm{rpm}\) is(a) 15(b) 18(c) 20(d) 60 .
Which one the following is the lubrication regime during normal operation of a rolling element bearing?(a) Hydrodynamic lubrication(b) Hydrostatic lubrication(c) Elastohydrodynamic lubrication(d) Boundary lubrication.
To carry a large axial load in a flat collar bearing, a number of collars is provided to(a) reduce frictional torque(b) increase frictional torque(c) decrease intensity of pressure(d) increase intensity of pressure.
The amount of energy absorbed by a flywheel is determined from the(a) torque-crank angle diagram(b) acceleration-crank angle diagram(c) speed-space diagram(d) speed-energy diagram.
Sensitiveness of a governor is defined as the ratio of the(a) maximum equilibrium speed to the minimum equilibrium speed(b) difference between maximum and minimum equilibrium speeds to the mean equilibrium speed(c) difference between maximum and minimum equilibrium speeds to the maximum equilibrium
A rigid rotor consists of a system of two masses located as shown in the given Fig.83.The system is (a) statically balanced (b) dynamically balanced (c) statically unbalanced (d) both statically and dynamically unbalanced. m2 = 2.5kg 10 cm, 10 cm 20 cm 10 cm 5 cm m = 10 kg Fig.83
A viscous damping system with free vibrations will be critically damped if the damping factor is(a) zero(b) less than one(c) equal to one(d) greater than one.
In a simple spring mass vibrating system, the natural frequency \(\omega_{n}\) of the system is \((k\) is spring stiffness, \(m\) is mass and \(m_{s}\) is spring mass)(a) \(\sqrt{\frac{k}{m-\frac{m_{s}}{3}}}\)(b) \(\sqrt{\frac{k}{m+\frac{m_{s}}{3}}}\)(c) \(\sqrt{\frac{k}{m+3 m_{s}}}\)(d)
A pulley and belt in a belt drive form a(a) cylindrical pair(b) turning pair(c) rolling pair(d) sliding pair
Match List I (Terms) with List II (Definitions) and select the correct answer using the codes given below the Lists: List I A. Module B. Addendum C. Circular pitch List II 1. Radial distance of a tooth from the pitch circle to the top of the tooth 2. Radial distance of a tooth from the pitch circle
The stiffness of spring \(k\) used in the Hartnell governor as shown in the given Fig. 84 ( \(F_{1}\) and \(F_{2}\) are centrifugal forces at maximum and minimum radii of rotation \(r_{1}\) and \(r_{2}\) respectively) is + a a a F-F (b) 2 b (d) 2 b 2(6) ( F + F 1-12 (a) 2 (c) 2 a a E-F 1-12 F + F
The balancing weights are introduced in planes parallel to the plane of rotation of the disturbing mass. To obtain complete dynamic balance, the minimum number of balancing weights to be introduced in different planes is(a) 1(b) 2(c) 3(d) 4 .
Consider the following statements:The unbalanced force in a single-cylinder reciprocating engine is 1). equal to inertia force of the reciprocating masses 2). equal to gas force 3). always fully balanced Which of the statements(s) is/are correct?(a) 1 alone(b) 2 alone(c) 1 and 3(d) 2 and 3 .
The equivalent spring stiffness for the system shown in the given Fig. 85 ( SS is the spring stiffness of each of the three springs) is(a) S2S2(b) S3S3(c) 2S22S2(d) SS. S S www m S wwww W Rigid bar Fig.85
Consider the following methods:1). Energy method 2). Equilibrium method 3). Rayleigh's method Which of these methods can be used for determining the natural frequency of the free vibrations?(a) 1 and 2(b) 1,2 , and 3(c) 1 and 3(d) 2 and 3 .
Consider the following statements:1). In forced vibrations, the body vibrates under the influence of an applied force 2). In damped vibrations, amplitude reduces over every cycle of vibration 3). In torsional vibrations, the disc moves parallel to the axis of shaft 4). In transvers vibrations, the
Consider the following specifications of gears A. B. C and D:Which of these gears form the pair of spur gears to achieve a gear ratio of 3 ?(a) A and B (b) A and D (c) BB and CC(d) CC and DD. Gears A B C D Numbers of teeth 20 60 20 60 Pressure angle 14 12 14 20 1412 Module 1 3 3 1 Material Steel
Minimum number of teeth for involute rack and pinion arrangement for pressure angle of \(20^{\circ}\) is(a) 18(b) 20(c) 30(d) 34 .
Rope brake dynamometer uses(a) water as lubricant(b) oil as lubricant(c) grease as lubricant(d) no lubricant.
Consider the following statements:If the fluctuation of speed during a cycle is \(\pm 5 \%\) of mean speed of a flywheel, the coefficient of fluctuation of speed will 1). increase with increase of mean speed of prime mover 2). decrease with increase of mean speed of prime mover 3). remain same with
Which one of the following "Kinematic pairs" has 3 degrees of freedom between the pairing elements? (a) (b) 2 1 (d) 2 2
The below Fig. 86 shows a four bar mechanism. If the radial acceleration of the point \(C\) is \(5 \mathrm{~cm} / \mathrm{s}^{2}\), the length of the link \(C D\) is(a) \(2 \mathrm{~cm}\)(b) \(10 \mathrm{~cm}\)(c) \(20 \mathrm{~cm}\)(d) \(100 \mathrm{~cm}\). v=10 cm/sec B Fig.86 D
A slider sliding at \(10 \mathrm{~cm} / \mathrm{s}\) on a link which is rotating at \(60 \mathrm{rpm}\). is subjected to Corioli's acceleration of magnitude(a) \(40 \pi^{2} \mathrm{~cm} / \mathrm{s}^{2}\)(b) \(0.4 \pi^{2} \mathrm{~cm} / \mathrm{s}^{2}\)(c) \(40 \pi \mathrm{cm} / \mathrm{s}^{2}\)(d)
Consider the following necessary and sufficient conditions for replacing a rigid body by a dynamical equivalent system of two masses:1). Total mass must be equal to that of the rigid body 2). Sum of the squares of radii of gyration of two masses about the c.g. of the rigid body must be equal to
Match List I (Mechanism) with List II (Name) and select the correct answer using the codes given below the lists: List I (Mechanism) A. Mechanism used to reproduce a diagram to an enlarged or reduced scale B. A straight line mechanism made up of turning pairs C. Approximate straight line motion
Consider the following mechanisms:1). Oscillating cylinder engine mechanism 2). Toggle mechanism 3). Radial cylinder engine mechanism 4). Quick Return Mechanism Which of the above are inversions of slider-crank mechanism?(a) 1,2 , and 4(b) 2,3 , and 4(c) 1,2 , and 3(d) 1,3 , and 4 .
The frictional torque transmitted in a flat pivot bearing, assuming uniform wear, is(a) \(\mu W R\)(b) \(\frac{3}{4} \mu W R\)(c) \(\frac{2}{3} \mu W R\)(d) \(\frac{1}{2} \mu W R\).(where \(\mu=\) Coefficient of friction\(W=\) Load over the bearing\(R=\) Radius of bearing)
With usual notations for different parameters involved, the maximum fluctuation of energy for a flywheel is given by(a) \(2 E C_{s}\)(b) \(\frac{E C_{s}}{2}\)(c) \(2 E C_{s}^{2}\)(d) \(2 E^{2} C_{s}\).
Hammer blow(a) is the maximum horizontal unbalanced force caused by the mass provided to balance the reciprocating masses(b) is the maximum vertical unbalanced force caused by the mass added to balance the reciprocating masses(c) varies as the square root of the speed(d) varies inversely with the
Whirling speed of shaft is the speed at which(a) shaft tends to vibrate in longitudinal direction(b) torsional vibrations occur(c) shaft tends to vibrate vigorously in transverse direction(d) combination of tranverse and longitudinal vibration occurs.
The velocity of sliding of meshing gear teeth is(a) \(\left(\omega_{1} \times \omega_{2}\right) x\)(b) \(\frac{\omega_{1}}{\omega_{2}} x\)(c) \(\left(\omega_{1} \times \omega_{2}\right) x\)(d) \(\left(\omega_{1}+\omega_{2}\right) x\)(where \(\omega_{1}\) and \(\omega_{2}\) = angular velocities of
A speed reducer unit consists of a double-threaded worm of pitch \(=11 \mathrm{~mm}\) and a worm wheel of pitch diameter \(=84 \mathrm{~mm}\). The ratio of the output torque to the input torque is(a) 7.6(b) 12(c) 24(d) 42 .

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