HPAS Maths Optional PYQs: Statics

On that page, you will find year-wise and question-wise solutions.

Statics questions focus on the study of bodies or particles at rest under the action of forces, including resultants, moments, stability, and frameworks.

HPAS 2024 Statics Questions

Question 7(b): \(R\) is the resultant of forces \(P\) and \(Q\) acting on a particle. If \(P\) is reversed, with \(Q\) remaining the same, the resultant becomes \(R’\). If \(R\) and \(R’\) are perpendicular to each other, show that \(\mathbf{P=Q}\).

HPAS 2023 Statics Questions

Question 7(b): Three forces \(P\), \(Q\), and \(R\) act on a particle and keep it in equilibrium. If the angle between \(P\) and \(Q\), and between \(Q\) and \(R\), is \(120^\circ\) each, then show that \(\mathbf{P=Q=R}\).

HPAS 2021 Statics Questions

Question 7(b): Three forces act perpendicular to the sides of a triangle at their middle points and are proportional to the sides. Show that \(\mathbf{they are in equilibrium}\).

Question 8(a): The resultant of two forces acts along a line perpendicular to one force and is in magnitude half the other. Compute the angle between the forces.

HPAS 2020 Statics Questions

Question 6(b): Define a wrench of a system of forces. Three forces \(P\), \(Q\), and \(R\) act along the three straight lines \(x=0, y-z=a\); \(y=0, z-x=a\); and \(z=0, x-y=a\) respectively. Find the vector symmetrical equation of the central axis and the pitch of the equivalent wrench.

Question 8(a): A heavy uniform rod rests with one end against a smooth vertical wall and with a point in its length resting on a smooth peg. Find the position of equilibrium, and show that it is unstable.

HPAS 2018 Statics Questions

Question 8(b): Three forces \(P\), \(Q\), and \(R\) act along the sides of the triangle taken in order, formed by the lines \(x+y=1\), \(y-x=1\), and \(y=2\). Find the equation of the line of action of their resultant.

HPAS 2017 Statics Questions

Question 7(a): Five weightless rods of equal length are jointed together to form a rhombus \(ABCD\) with one diagonal \(BD\). If a weight \(W\) is attached to \(C\) and the system is suspended from \(A\), show that there is a thrust in BD equal to \(\frac{W}{\sqrt{3}}\).

Question 7(b): Two forces act, one along the line \(y=0, z=0\) and the other along the line \(x=0, z=c\). As the forces vary, show that the surface generated by the central axis of their equivalent wrench is \((x^2+y^2)z = cy^2\).

HPAS 2016 Statics Questions

(No dedicated Statics questions were found in the provided excerpts for 2016.)

HPAS 2015 Statics Questions

Question 1(f): Forces 13, 10 and 5 kg weight act along the sides \(BC\), \(CA\) and \(AB\) of an equilateral triangle \(ABC\). Find the direction and the magnitude of their resultant.

Question 8(a): Six equal heavy rods, freely hinged at their ends form a regular hexagon \(ABCDEF\) which when hung-up by the point \(A\) is kept from altering its shape by two light rods \(BF\) and \(CE\). Find the thrusts of these rods.

HPAS 2014 Statics Questions

Question 1(f): Two rods, each of length \(2a\), have their ends united at an angle \(\alpha\), and are placed in a vertical plane on a sphere of radius \(r\). Prove that the equilibrium is stable or unstable according as \(\sin~\alpha>or<\frac{2r}{a}\).

Question 8(a): The moments of a given system of coplanar forces about three points: \((2,0)\), \((0, 2)\) and \((2, 2)\) in their plane are 3, 4 and 10 units respectively. Find the magnitude of the resultant force and the equation of its line of action.