JEE Main & Advanced Physics Simple Harmonic Motion Question Bank

done Velocity of Simple Harmonic Motion Total Questions - 27

• question_answer1)
  A simple pendulum performs simple harmonic motion about X = 0 with an amplitude A and time period T. The speed of the pendulum at \[X=\frac{A}{2}\] will be                                       [MP PMT 1987]
  A)
             \[\frac{\pi A\sqrt{3}}{T}\]       done clear
  B)
             \[\frac{\pi A}{T}\] done clear
  C)
             \[\frac{\pi A\sqrt{3}}{2T}\]     done clear
  D)
             \[\frac{3{{\pi }^{2}}A}{T}\] done clear
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• question_answer2)
  A body is executing simple harmonic motion with an angular frequency \[2rad/s\]. The velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, is                            [Pb. CET 1996; Pb. PMT 1997; AFMC 1998;  CPMT 1999]
  A)
             40 mm /s                                done clear
  B)
             \[60mm/s\] done clear
  C)
             \[113mm/s\]                         done clear
  D)
             \[120mm/s\] done clear
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• question_answer3)
  A body of mass 5 gm is executing S.H.M. about a point with amplitude 10 cm. Its maximum velocity is 100 cm/sec. Its velocity will be 50 cm/sec at a distance                [CPMT 1976]
  A)
             5     done clear
  B)
             \[5\sqrt{2}\] done clear
  C)
             \[5\sqrt{3}\]                          done clear
  D)
             \[10\sqrt{2}\] done clear
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• question_answer4)
  A simple harmonic oscillator has a period of 0.01 sec and an amplitude of 0.2 m. The magnitude of the velocity in \[m{{\sec }^{-1}}\] at the centre of oscillation is [JIPMER 1997]
  A)
             \[20\pi \]                                done clear
  B)
             100 done clear
  C)
             40p done clear
  D)
             \[100\pi \] done clear
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• question_answer5)
  A particle executes S.H.M. with a period of 6 second and amplitude of 3 cm. Its maximum speed in cm/sec is                    [AIIMS 1982]
  A)
             \[\pi /2\]                                 done clear
  B)
             \[\pi \] done clear
  C)
             \[2\pi \]                                   done clear
  D)
             \[3\pi \] done clear
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• question_answer6)
  A particle is executing S.H.M. If its amplitude is 2 m and periodic time 2 seconds, then the maximum velocity of the particle will be                                                            [MP PMT 1985]
  A)
             \[\pi \,m/s\]                          done clear
  B)
             \[\sqrt{2\pi }\,m/s\] done clear
  C)
             \[2\pi \,m/s\]                       done clear
  D)
             \[4\pi \,m/s\] done clear
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• question_answer7)
  A S.H.M. has amplitude ?a? and  time period T. The maximum velocity will be [MP PMT 1985; CPMT 1997; UPSEAT 1999]
  A)
             \[\frac{4a}{T}\]                    done clear
  B)
             \[\frac{2a}{T}\] done clear
  C)
             \[2\pi \sqrt{\frac{a}{T}}\] done clear
  D)
             \[\frac{2\pi a}{T}\] done clear
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• question_answer8)
  A body is executing S.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is          [CPMT 1991; MP PET 1995]
  A)
             \[2\pi \,sec\]                         done clear
  B)
             \[\pi /2\]sec done clear
  C)
             \[\pi \,sec\]                           done clear
  D)
             \[3\pi /2\,sec\] done clear
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• question_answer9)
  A particle has simple harmonic motion. The equation of its motion is \[x=5\sin \left( 4t-\frac{\pi }{6} \right)\], where x is its displacement. If the displacement of the particle is 3 units, then it velocity is [MP PMT 1994]
  A)
             \[\frac{2\pi }{3}\]                done clear
  B)
             \[\frac{5\pi }{6}\] done clear
  C)
             \[20\]                                       done clear
  D)
             \[16\] done clear
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• question_answer10)
  If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 sec, then its maximum velocity is                    [AIIMS 1998; MH CET 2000; DPMT 2000]
  A)
             0.10 m / s                                done clear
  B)
             0.15 m / s done clear
  C)
             0.8 m / s                                  done clear
  D)
             0.26 m / s done clear
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• question_answer11)
  If the displacement of a particle executing SHM is given by \[y=0.30\sin (220t+0.64)\] in metre, then the frequency and maximum velocity of the particle is              [AFMC 1998]
  A)
             35 Hz, 66 m / s                      done clear
  B)
             45 Hz, 66 m / s done clear
  C)
             58 Hz, 113 m / s                    done clear
  D)
             35 Hz, 132 m / s done clear
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• question_answer12)
  The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator are \[2\,m/s\] and \[4\,m/{{s}^{2}}.\] Then angular velocity will be [Pb. PMT 1998; MH CET 1999, 2003]
  A)
             3 rad/sec                                done clear
  B)
             0.5 rad/sec done clear
  C)
             1 rad/sec                                done clear
  D)
             2 rad/sec done clear
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• question_answer13)
  If a particle under S.H.M. has time period 0.1 sec and amplitude \[{{\tan }^{-1}}\frac{a}{g}\]. It has maximum velocity                                                                                                [RPET 2000]
  A)
             \[\frac{\pi }{25}\,m/s\]     done clear
  B)
             \[\frac{\pi }{26}\,m/s\] done clear
  C)
             \[{{\tan }^{-1}}\frac{a}{g}\]    done clear
  D)
             None of these done clear
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• question_answer14)
  A particle executing simple harmonic motion has an amplitude of 6 cm. Its acceleration at a distance of 2 cm from the mean position is \[8\,cm/{{s}^{2}}\]. The maximum speed of the particle is          [EAMCET (Engg.) 2000]
  A)
             8 cm/s                                      done clear
  B)
             12 cm/s done clear
  C)
             16 cm/s                                   done clear
  D)
             24 cm/s done clear
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• question_answer15)
  A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position the velocity of the particle is 10 cm/s. The distance of the particle from the mean position when its speed becomes 5 cm/s is [EAMCET (Med.) 2000]
  A)
             \[\sqrt{3}\,cm\]                   done clear
  B)
             \[\sqrt{5}\,cm\] done clear
  C)
             \[2(\sqrt{3})\,cm\]             done clear
  D)
             \[2(\sqrt{5})\,cm\] done clear
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• question_answer16)
  Two particles P and Q start from origin and execute Simple Harmonic Motion along X-axis with same amplitude but with periods 3 seconds and 6 seconds respectively. The ratio of the velocities of P and Q when they meet is  [EAMCET 2001]
  A)
             1 : 2                                           done clear
  B)
             2 : 1 done clear
  C)
             2 : 3                                           done clear
  D)
             3 : 2 done clear
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• question_answer17)
  A particle is performing simple harmonic motion with amplitude A and angular velocity w. The ratio of maximum velocity to maximum acceleration is         [Kerala (Med.) 2002]
  A)
             w    done clear
  B)
             1/w done clear
  C)
             w2   done clear
  D)
             Aw done clear
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• question_answer18)
  The angular velocities of three bodies in simple harmonic motion are \[{{\omega }_{1}},\,{{\omega }_{2}},\,{{\omega }_{3}}\] with their respective amplitudes as \[{{A}_{1}},\,{{A}_{2}},\,{{A}_{3}}\]. If all the three bodies have same mass and velocity, then                                                           [BHU 2002]
  A)
             \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\]  done clear
  B)
             \[{{A}_{1}}{{\omega }_{1}}^{2}={{A}_{2}}{{\omega }_{2}}^{2}={{A}_{3}}{{\omega }_{3}}^{2}\] done clear
  C)
             \[{{A}_{1}}^{2}{{\omega }_{1}}={{A}_{2}}^{2}{{\omega }_{2}}={{A}_{3}}^{2}{{\omega }_{3}}\]         done clear
  D)
             \[{{A}_{1}}^{2}{{\omega }_{1}}^{2}={{A}_{2}}^{2}{{\omega }_{2}}^{2}={{A}^{2}}\] done clear
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• question_answer19)
  The velocity of a particle performing simple harmonic motion, when it passes through its mean position is                    [MH CET (Med.) 2002; BCECE 2004]
  A)
             Infinity                                     done clear
  B)
             Zero done clear
  C)
             Minimum                               done clear
  D)
             Maximum done clear
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• question_answer20)
  The velocity of a particle in simple harmonic motion at displacement y from mean position is [BCECE 2003; RPMT 2003]
  A)
             \[\omega \sqrt{{{a}^{2}}+{{y}^{2}}}\]                            done clear
  B)
             \[\omega \sqrt{{{a}^{2}}-{{y}^{2}}}\] done clear
  C)
             \[\omega y\]                        done clear
  D)
             \[{{\omega }^{2}}\sqrt{{{a}^{2}}-{{y}^{2}}}\] done clear
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• question_answer21)
  A particle is executing the motion \[x=A\cos (\omega \,t-\theta )\]. The maximum velocity of the particle is  [BHU 2003; CPMT 2004]
  A)
             \[A\omega \cos \theta \]        done clear
  B)
             \[A\omega \] done clear
  C)
             \[A\omega \sin \theta \] done clear
  D)
             None of these done clear
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• question_answer22)
  A particle executing simple harmonic motion with amplitude of 0.1 m. At a certain instant when its displacement is 0.02 m, its acceleration is 0.5 m/s2. The maximum velocity of the particle is (in m/s)                                          [MP PET 2003]
  A)
             0.01                                           done clear
  B)
             0.05 done clear
  C)
             0.5  done clear
  D)
             0.25 done clear
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• question_answer23)
  The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes \[8\sqrt{3}cm/s,\]will be [Pb. PET 2003]
  A)
             \[2\sqrt{3}cm\]                    done clear
  B)
             \[\sqrt{3}cm\] done clear
  C)
             1 cm                                          done clear
  D)
             2 cm done clear
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• question_answer24)
  The maximum velocity of a simple harmonic motion represented by \[y=3\sin \,\left( 100\,t+\frac{\pi }{6} \right)\]is given by  [BCECE 2005]
  A)
             300 done clear
  B)
             \[\frac{3\pi }{6}\] done clear
  C)
             100 done clear
  D)
             \[\frac{\pi }{6}\] done clear
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• question_answer25)
  The displacement equation of a particle is \[x=3\sin 2t+4\cos 2t.\] The amplitude and maximum velocity will be respectively                                                                     [RPMT 1998]
  A)
             5, 10                                          done clear
  B)
             3, 2 done clear
  C)
             4, 2 done clear
  D)
             3, 4 done clear
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• question_answer26)
  Velocity at mean position of a particle executing S.H.M. is v, they velocity of the particle at a distance equal to half of the amplitude                                                                 [RPMT 2001]
  A)
             4v   done clear
  B)
             2v done clear
  C)
             \[\frac{\sqrt{3}}{2}v\]       done clear
  D)
             \[\frac{\sqrt{3}}{4}v\] done clear
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• question_answer27)
  The instantaneous displacement of a simple pendulum oscillator is given by \[x=A\cos \left( \omega t+\frac{\pi }{4} \right)\]. Its speed will be maximum at time                                                        [CPMT 2000]
  A)
             \[\frac{\pi }{4\omega }\] done clear
  B)
             \[\frac{\pi }{2\omega }\] done clear
  C)
             \[\frac{\pi }{\omega }\]          done clear
  D)
             \[\frac{2\pi }{\omega }\] done clear
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