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A particle moves in a straight line and its position is defined by the equation x = 6 t² - t3 where t is expressed in seconds and x in meters. The maximum velocity during the motion is
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ω rad/sec is the angular velocity of a crank whose radius is r. If it makes θ° with inner dead centre and obliquity of the connecting rod l is , the velocity v of the piston, is given by the equation
A. ω2 (l cos + r sin tan θ)
B. ω2 (l sin + r cos φ tan θ)
C. ω (l sin + r cos tan θ)
D. ω2 (l sin - r cos θ tan )
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4
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 mechanical advantage of the lifting machine is
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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. A simple harmonic motion
B. A rectilinear motion with constant speed
C. A damped oscillatory motion
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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
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A flywheel of moment of inertia 20 kgm is acted upon by a tangential force of 5 N at 2 m from its axis, for 3 seconds. The increase in angular velocity in radian per second is
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The angles between two forces to make their resultant a minimum and a maximum respectively are
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Parallelogram Law of Forces states, if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by
C. The diagonal of the parallelogram which does not pass through the point of intersection of the forces
D. The diagonal of the parallelogram which passes through the point of intersection of the forces
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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
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A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec. The work required to stop the hoop is
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If two forces of 3 kg and 4 kg act at right angles to each other, their resultant force will be equal to
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The velocity ratio of the differential wheel and axle is
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The point about which combined motion of rotation and translation of a rigid body takes place, is known as
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The centre of gravity of a triangle is at the point where three
A. Medians of the triangle meet
B. Perpendicular bisectors of the sides of the triangle meet
C. Bisectors of the angle of the triangle meet
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The vertical reaction at the support A of the structure shown in below figure, is
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A system of coplanar forces is in equilibrium when
B. Funicular polygon closes
C. Both force polygon and funicular polygon close
D. All the forces are concurrent
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If a particle is projected inside a horizontal tunnel which is 554 cm high with a velocity of 60 m per sec, the angle of projection for maximum range, is
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M.I. of a thin ring (external diameter D, internal diameter d) about an axis perpendicular to the plane of the ring, is
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If the tension in a cable supporting a lift moving upwards is twice the tension when the lift is moving downwards, the acceleration of the lift, is
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The angular speed of a car while taking a circular turn of radius 100 m at 36 km/hour, is
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A 49 kg lady stands on a spring scale in an elevator. During the first 5 sec, starting from rest, the scale reads 69 kg. The velocity of the elevator will be
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The resolved part of the resultant of two forces inclined at an angle θ in a given direction is
A. Algebraic sum of the resolved parts of the forces in the direction
B. Arithmetical sum of the resolved parts of the forces in the direction
C. Difference of the forces multiplied by cosine θ°
D. Sum of the forces multiplied by the tangent θ°
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A weight of 100 kg is supported by a string whose ends are attached to pegs A and B at the same level shown in below figure. The tension in the string is
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The moment of inertia of a hollow circular section whose external diameter is 8 cm and internal diameter is 6 cm, about centroidal axis, is
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0.For maximum range of a projectile, the angle of projection should be
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For a non-concurrent force system to be in equilibrium
A. Only the closure of force polygon is sufficient
B. Only the closure of funicular polygon is sufficient
C. Both force polygon and funicular polygon must close
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Time of flight of a projectile on a horizontal plane, is
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One half of a vibration of a body, is called
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The reaction RB of the roller support B of the beam shown in below figure is
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The piston of a steam engine moves with a simple harmonic motion. The crank rotates 120 r.p.m. and the stroke length is 2 metres. The linear velocity of the piston when it is at a distance of 0.5 metre from the centre, is