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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

हिन्दी

In the system shown in Figure, a uniform bar AB of length 70 cm and weight \( W \) is supported on knife edges \( K_1 \) and \( K_2 \) located at 10 cm from ends A and B respectively. A load \( W_1 \) is suspended at P, 30 cm from end A. If the reactions at \( K_1 \) and \( K_2 \) are denoted as \( R_1 \) and \( R_2 \), taking the moments about the centre of gravity G of the bar yields which of the following equilibrium conditions?

  1. \( R_1(K_1G) - W_1(PG) - R_2(K_2G) = 0 \)
  2. \( R_1(K_1G) + W_1(PG) - R_2(K_2G) = 0 \)
  3. \( -R_1(K_1G) - W_1(PG) + R_2(K_2G) = 0 \)
  4. \( -R_1(K_1G) + W_1(PG) + R_2(K_2G) = 0 \)

Correct answer · Option 4

\( -R_1(K_1G) + W_1(PG) + R_2(K_2G) = 0 \)

Explanation

Taking moments about G: \( R_1 \) produces a clockwise (negative) moment, while \( W_1 \) and \( R_2 \) produce anticlockwise (positive) moments, giving \( -R_1(K_1G) + W_1(PG) + R_2(K_2G) = 0 \).
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