Home › Previous year questions › GATE 2021 PI › Question 60GATE 2021 PI – Question 60 General Engineering · Applied Mechanics · 2 marks · Numerical answer
A 30 kg smooth rigid sphere rests on two frictionless rigid inclines, left at 60° and right at 30° to horizontal, as shown. Use g = 9.81 m/s². Find contact force at A in N to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation Correct answer: 147.00 to 147.30
Explanation Reactions are normal to the surfaces. Horizontal balance gives $N_A\cos30^\circ=N_B\cos60^\circ$, so N_B = √3 N_A. Vertical balance gives $N_A\sin30^\circ+N_B\sin60^\circ=mg$, hence 0.5N_A+1.5N_A = 294.3. Thus **N_A = 147.15 N**.
More Applied Mechanics questions GATE 2021 PI Q61 – The shown rigid members AB,BC,CA form an equilateral truss, with pin A and frictionless… GATE 2026 PI Q21 – The ratio of hydrostatic stress to volumetric strain is called . GATE 2026 PI Q55 – A homogeneous isotropic linear-elastic cylindrical component of diameter 10 mm is under… GATE 2025 PI Q25 – A simply supported beam AB of span L has an applied moment M at C, distance a from A, as… GATE 2025 PI Q26 – Relate hoop stress σ₁ and longitudinal stress σ₂ in a closed thin cylindrical pressure… GATE 2025 PI Q29 – Principal stresses are 300,250,100 MPa. Yielding is just beginning. Find yield strength… All Applied Mechanics questions →
