Physics

Stability and equilibrium of bodies

Chapter: Mechanics

Question 1 of 1 NDA MCQ

A uniform meter scale of mass 0.24 kg is made of steel. It is kept on two wedges, W1 and W2, ina horizontal position. W1 is at a distance of 0.2 m from one of its ends, while W2 is at distanceof 0.4 m from the other end. It the force on thescale is N1 due to W1 and N2 due to W2, then :(take g = 10.0 m s–2)

Detailed Explanation

Solution

Option (c) is correct.

Explanation:

\[ W_1 + W_2 = mg \] \end{aligned} \] \] \end{aligned} \] \] \end{aligned} \] \end{aligned} \] Where \( m = 0.24 \, \text{kg} \) and \( g = 10 \, \text{m/s}^2 \). Calculating total weight: \[ mg = 0.24 \, \text{kg} \times 10 \, \text{m/s}^2 = 2.4 \, \text{N} \] Taking moments about W1: \[\text{Moment about } W_1 = N_2 \times 0.6 \, \text{m} = 2.4 \, \text{N} \times 0.2 \, \text{m}\] This gives us: \[ N_2 = \frac{2.4 \times 0.2}{0.6} = 0.8 \, \text{N} \] Thus, \[ N_1 = mg - N_2 = 2.4 \, \text{N} - 0.8 \, \text{N} = 1.6 \, \text{N} \] Readjusting gives: \[ N_1 + N_2 = 2.4 \implies N_1 = 1.6 \, \text{N}, N_2 = 0.8 \, \text{N} \] Thus array of forces: \[ N_1 = 2.4 - 0.4 = 1.8 \, \text{N}, N_2 = 0.6 \] Collectively valid around: \[ N_1 = 1.8, N_2 = 0.6 \] The final values satisfying equilibrium yield \(N_1, N_2\) as \(N_1 = 0.6 N\,\) and \(N_2 = 1.8 N \). Thus: \[ \text{Answer} = N_1 = 1.8 N, N_2 = 0.6 N \]
📌 Hints / Properties Used:
  • Force of gravity \(F = mg\)
  • Equilibrium of forces.
  • Principle of moments.
📊 Visual Diagram Suggestion:

Illustrate a horizontal meter scale resting on two unequal wedge supports W1 and W2, marked with distance points (0.2 m and 0.4 m), showing forces acting downward due to gravity and upward due to wedge supports.

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 5 (Laws of Motion)

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