2. Calculate the work done by the force F = 5zi + xyj + x^2zk with the line integral ∫_C F · dr from point (0, 0, 0) to point (1, 1, 1) along the following two paths (a) straight line : x = y, y = z and (b) parabolic curve : x = y, z = y^2.(25%)

1. A slender rod of length l is pivoted about a Point C located at a distance b from its center G. It is released from rest in a horizontal position and swings freely. Determine (a) the distance b for which the angular velocity of the rod as it passes through a vertical position is maximum, (b) the corresponding values of its angular velocity and of the reaction at C.(25%)

2. Calculate the work done by the force \( F = 5zi + xyj + x^2zk \) with the line integral \( \int_C F \cdot dr \) from point \( (0, 0, 0) \) to point \( (1, 1, 1) \) along the following two paths (a) straight line : \( x = y \), \( y = z \) and (b) parabolic curve : \( x = y \), \( z = y^2 \).(25%)

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