1 Advanced Mathematics • Statics The Cartesian equation of common catenary is: The Cartesian equation of common catenary is: सेव करें Save सेव्ड Saved A. y = c sinh(x/c) y = c sinh(x/c) B. y = c cosh(x/c) y = c cosh(x/c) C. y = c coth(x/c) y = c coth(x/c) D. y = c tanh(x/c) y = c tanh(x/c) उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: B Correct Answer: B The curve formed by a uniform flexible chain hanging under its own weight is the catenary y = c cosh(x/c). The curve formed by a uniform flexible chain hanging under its own weight is the catenary y = c cosh(x/c).
2 Advanced Mathematics • Statics If P and Q are two non-intersecting forces whose directions are perpendicular, then the ratio of the distances of the central axis from their lines of action is represented as: If P and Q are two non-intersecting forces whose directions are perpendicular, then the ratio of the distances of the central axis from their lines of action is represented as: सेव करें Save सेव्ड Saved A. Q^2 : 2P^2 Q^2 : 2P^2 B. 2P^2 : Q^2 2P^2 : Q^2 C. Q^2 : P^2 Q^2 : P^2 D. P^2 : Q^2 P^2 : Q^2 उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: C Correct Answer: C For two perpendicular non-intersecting forces, the distances of the central axis from their respective lines of action are in the inverse-square ratio of the forces, giving Q^2 : P^2 in the stated order. For two perpendicular non-intersecting forces, the distances of the central axis from their respective lines of action are in the inverse-square ratio of the forces, giving Q^2 : P^2 in the stated order.
3 Advanced Mathematics • Statics Two equal uniform rods AB and AC, each of length 2b, are freely joined at A and rest on a smooth vertical circle of radius a. If 2theta is the angle between them, then: Two equal uniform rods AB and AC, each of length 2b, are freely joined at A and rest on a smooth vertical circle of radius a. If 2theta is the angle between them, then: सेव करें Save सेव्ड Saved A. a sin^3(theta)=b cos(theta) a sin^3(theta)=b cos(theta) B. b sin^2(theta)=a cos(theta) b sin^2(theta)=a cos(theta) C. a sin^2(theta)=b cos(theta) a sin^2(theta)=b cos(theta) D. b sin^3(theta)=a cos(theta) b sin^3(theta)=a cos(theta) उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: D Correct Answer: D Applying the equilibrium condition to the symmetric rod configuration gives b sin^3(theta)=a cos(theta), as marked in the source paper. Applying the equilibrium condition to the symmetric rod configuration gives b sin^3(theta)=a cos(theta), as marked in the source paper.
4 Advanced Mathematics • Statics A solid frustum of a paraboloid of revolution of height h and latus rectum 4a rests with its vertex on the vertex of a paraboloid of revolution whose latus rectum is 4b. The equilibrium is stable if: A solid frustum of a paraboloid of revolution of height h and latus rectum 4a rests with its vertex on the vertex of a paraboloid of revolution whose latus rectum is 4b. The equilibrium is stable if: सेव करें Save सेव्ड Saved A. h < 3ab/(a+b) h < 3ab/(a+b) B. h < 2ab/(a+b) h < 2ab/(a+b) C. h > ab/(a+b) h > ab/(a+b) D. h > 3ab/(a+b) h > 3ab/(a+b) उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: A Correct Answer: A The stability condition obtained by comparing the centre-of-gravity displacement with the supporting-paraboloid geometry is h<3ab/(a+b). The stability condition obtained by comparing the centre-of-gravity displacement with the supporting-paraboloid geometry is h<3ab/(a+b).