GATE Mechanical Engineering (ME) 2016 Shift 2 Solved Paper

Question : 41 of 65

Marks: +1, -0

A system of particles in motion has mass center G as shown in the figure. The particle i has mass m_i and its position with respect to a fixed point O is given by the position vector r_i. The position of the particle with respect to G is given by the vector ρ_i. The time rate of change of the angular momentum of the system of particles about G is
(The quantity

ρ ↖{¨}↙{i}

indicates the second derivative of ρ_i with respect to time and likewise for r_i)

$∑ ↙{{i}r}↖{{i}} × m_{i}ρ ↖{¨}↙{i}$
$∑ \limits_{i}ρ _{i} × m_{i}r↖{¨}↙{i}$
$∑ ↙{{i}r}↖{{i}} × m_{i}r↖{¨}↙{i}$
$∑ \limits_{i}ρ _{i} × m_{i}ρ ↖{¨}↙{i}$

Validate

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