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GATE ME 2016 Set 2 — Question 41

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MCQ+2 / -0.67HardLinear & Angular Impulse-MomentumDynamicsEngineering Mechanics

Engineering Mechanics → Dynamics → Linear & Angular Impulse-Momentum

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Question

A system of particles in motion has mass center GG as shown in the figure. The particle ii has mass mim_i and its position with respect to a fixed point OO is given by the position vector rir_i. The position of the particle with respect to GG is given by the vector ρi\rho_i. The time rate of change of the angular momentum of the system of particles about GG is
(The quantity ρ¨i\ddot{\rho}_i indicates second derivative of ρi\rho_i with respect to time and likewise for rir_i).
A system of particles with mass center G, fixed point O, and vectors r_i and rho_i
  1. A.
    ∑iri×miρ¨i\sum_i r_i \times m_i \ddot{\rho}_i
  2. B.
    ∑iρi×mir¨i\sum_i \rho_i \times m_i \ddot{r}_i
  3. C.
    ∑iri×mir¨i\sum_i r_i \times m_i \ddot{r}_i
  4. D.
    ∑iρi×miρ¨i\sum_i \rho_i \times m_i \ddot{\rho}_i

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