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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show `p=p'_1+m_iV` where pi is the momentum of the ith particle (of mass `m_i`) and `p′_i = m_iv′_i`. Note `v′_i` is the velocity of the ith
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show K=K'+1/2M`V^2` where K is the total kinetic energy of the system of particles, K′ is the total kinetic energy of the system when the particle
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show where `L'=r'_1xxp'_1` is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember `r'1=r_1-R`;
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show `(dL')/(dt)=sum r'_1xx(dp')/(dt)` Further, show that `(dL')/(dt)=τ'_(ext)` where `τ'_(ext)` is the sum of all external torques acting on the system about the centre of mass. (Hint
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The displacement of a particle is represented by the equation `y = 3 cos (pi/ 4 - ωt)` . The motion of the particle
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The displacement of a particle is represented by the equation `y = sin^3 ωt` . The motion
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The relation between acceleration and displacement of four particles are given
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Motion of an oscillating liquid column in a U-tube
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A particle is acted simultaneously by mutually perpendicular simple hormonic motions `x = a cos ωt and y = a sin ωt` . The trajectory of motion of the particle will
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The displacement of a particle varies with time according to the relation `y = a sin ωt + b cos
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Four pendulums A, B, C and D are suspended from the same elastic support as shown in Fig. . A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse
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Fig. shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P
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The equation of motion of a particle is `x = a cos (α t )^ 2` . The motion
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A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2 . The period of oscillation
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When a mass m is connected individually to two springs S1 and S2 , the oscillation frequencies are ν 1 and ν 2 . If the same mass is attached to the two springs as shown in Fig. , the oscillation frequency would
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The rotation of earth about its axis
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Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point
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Displacement vs. time curve for a particle executing S.H.M. is shown in Fig. Choose the correct
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Which of the following statements is/are true for a simple harmonic
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The displacement time graph of a particle executing S.H.M. is shown in Fig. Which of the following statement is/are
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