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Machine Kinematics Multiple Choice Questions and Answers – Centre of Percussion

(1) The piston of a steam engine moves with simple harmonic motion. The crank rotates at 120 r.p.m. with a stroke of 2 metres. Find the velocity of the piston, when it is at a distance of 0.75 metre from the centre.
[A] 8 m/s
[B] 8.31 m/s
[C] 9 m/s
[D] none of the mentioned
Answer: 8.31 m/s
(2) The piston of a steam engine moves with simple harmonic motion. The crank rotates at 120 r.p.m. with a stroke of 2 metres. Find the acceleration of the piston, when it is at a distance of 0.75 metre from the centre.
[A] 118.46 m/s2
[B] 90 m/s2
[C] 100 m/s2
[B] none of the mentioned
Answer: 118.46 m/s2

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(3) Law of isochronism
[A] states the time period (tp ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.
[B] states the time period (tp ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude (θ) does not exceed 4°.
[C] states the time period (tp) of a simple pendulum is directly proportional to √L , where L is the length of the string.
[D] none of the mentioned
Answer: states the time period (tp ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude (θ) does not exceed 4°.
(4) Law of mass
[A] states the time period (tp ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.
[B] states the time period (tp ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude (θ) does not exceed 4°.
[C] states the time period (tp ) of a simple pendulum is directly proportional to √L , where L is the length of the string.
[D] none of the mentioned
Answer: states the time period (tp ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.
(5) Law of length
[A] states the time period (tp ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.
[B] states the time period (tp ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude (θ) does not exceed 4°.
[C] states the time period (tp) of a simple pendulum is directly proportional to √L , where L is the length of the string.
[D] none of the mentioned
Answer: states the time period (tp) of a simple pendulum is directly proportional to √L , where L is the length of the string.
(6) Law of gravity
[A] states the time period (tp ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.
[B] states the time period (tp ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude (θ) does not exceed 4°.
[C] states the time period (tp) of a simple pendulum is directly proportional to √L , where L is the length of the string.
[D] states the time period (tp ) of a simple pendulum is inversely proportional to √g , where g is the acceleration due to gravity.
Answer: states the time period (tp ) of a simple pendulum is inversely proportional to √g , where g is the acceleration due to gravity.
(7) A helical spring, of negligible mass, and which is found to extend 0.25 mm under a mass of 1.5 kg, is made to support a mass of 60 kg. The spring and the mass system is displaced vertically through 12.5 mm and released. Determine the frequency of natural vibration of the system.
[A] 6 Hz
[B] 4.98 Hz
[C] 5.98 Hz
[D] none of the mentioned
Answer: 4.98 Hz
(8) A helical spring, of negligible mass, and which is found to extend 0.25 mm under a mass of 1.5 kg, is made to support a mass of 60 kg. The spring and the mass system is displaced vertically through 12.5 mm and released. Find the velocity of the mass, when it is 5 mm below its rest position.
[A] 0.36 m/s
[B] 0.46 m/s
[B] 0.56 m/s
[B] none of the mentioned
Answer: 0.36 m/s

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