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Forces of 1, 2 unit act along the lines x = 0 and y = 0. The equation of the line of action of the resultant is

1) y - 2x = 0 2) 2y - x = 0 3) y + x = 0 4) y - x = 0 Solution: (2) 2y - x = 0 It is by the resolution of force. The equation of the line of... View Article

If the forces of 12, 5 and 13 unit-wt balance at a point, two of them are inclined at

1) 30° 2) 45° 3) 90° 4) 60° Solution: (3) 90° R2 = P2 + Q2 + 2PQ cos ɑ (13)2 = (12)2 + (5)2 + 2 * 12 * 5 cos ɑ cos ɑ = 0 ɑ = π / 2... View Article

In a triangle ABC, 3 forces of magnitudes 3 AB, 2 AC and 6 CB are acting along the sides AB, AC and CB respectively. If the resultant meets AC at D, then the ratio DC : AD =

1) 1 : 1 2) 1 : 2 3) 1 : 3 4) 1 : 4 Solution: (2) 1 : 2 From the figure, it is clear that DC : AD = 1 : 2... View Article

When a particle be kept at rest under the action of the following forces

1) ↑ 8N, ↑ 5N, ↓ 13N 2) ↑ 7N, ↑ 4N, ↓ 12N 3) ↑ 5N, ↑ 8N, ↓ 10N 4) ↑ 4N, ↑ 2 √5 N, ↓ 6N Solution: (1) ↑ 8N, ↑ 5N, ↓ 13N Since 8N + 5N = 13N... View Article

If the resultant of two forces is of magnitude P and equal to one of them and perpendicular to it, then the other force is

1) P √2 2) P 3) P √3 4) None of these Solution: (1) P √2 |AB| = |Q| = √P2 + P2 = P √2... View Article

The sum of the two forces is 18 and their resultant perpendicular to the lesser of the forces is 12, then the lesser force is

1) 5 2) 3 3) 7 4) 15 Solution: (1) 5 Let the two forces P and Q be inclined at an angle ɑ. Then P + Q = 18 and resultant = 12 ---- (i) P2 +... View Article

The resultant R of two forces P and Q act at right angles to P. Then the angle between the forces is

1) cos-1 (P / Q) 2) cos-1 (- P / Q) 3) sin-1 (P / Q) 4) sin-1 (- P / Q) Solution: (2) cos-1 (- P / Q) Let ɑ be the angle between the forces... View Article

A horizontal force F is applied to a small object P of mass m on a smooth plane inclined to the horizon at an angle θ. If F is just enough to keep P in equilibrium, then F =

1) mg cos2 θ 2) mg sin2 θ 3) mg cosθ 4) mg tan θ Solution: (4) mg tan θ By applying Lami’s theorem at P, R / (sin 90o) = F / sin (180 -... View Article

Let R be the resultant of P and Q and if (P / 3) = (Q / 7) = (R / 5), then the angle between P and R is

1) cos-1 (11 / 14) 2) cos-1 (- 11 / 14) 3) 2π / 3 4) 5π / 6 Solution: (3) 2π / 3 (P / 3) = (Q / 7) = (R / 5) = λ (let) P = 3λ, Q = 7λ, R =... View Article

The resultant of two forces P and Q acting at an angle θ is equal to (2m + 1) √P² + Q², when they act at an angle 90 – θ, the resultant is (2m – 1) (√P² + Q²); then tan θ =

1) 1 / m 2) [m + 1] / [m - 1] 3) [m - 1] / [m + 1] 4) √1 + m2 Solution: (3) [m - 1] / [m + 1] Here, {(2m + 1) (√P2 + Q2}2 = P2 + Q2 + 2PQ... View Article

Three forces of magnitude 30, 60 and P acting at a point are in equilibrium. If the angle between the first two is 60°, the value of P is

1) 30 √7 2) 30 √3 3) 20 √6 4) 25 √2 Solution: (1) 30 √7 Since the forces are in equilibrium. Thus one of force must be equal in magnitude... View Article

The direction of three forces 1 N, 2 N and 3 N acting at a point are parallel to the sides of an equilateral triangle taken in order. The magnitude of their resultant is

1) (√3 / 2) N 2) 3 N 3) √3 N 4) (3 / 2) N Solution: (3) √3 N F1 = 1i F2 = (- 2 / 2) i + (2 √3 / 2) j and F3 = (- 3 / 2) i - (3 √3 / 2) j F... View Article

The resultant of two force P N and 3 N is a force of 7 N.If the direction of 3N force were reversed, the resultant would be √19. N. The value of P is

1) 5 N 2) 6 N 3) 3 N 4) 4 N Solution: (1) 5 N 72 = P2 + 32 + 2 * 3 * P cos θ --- (i) (√19)2 = P2 + (- 3)2 + 2 * (- 3) * P cos θ ----... View Article

The greatest and least magnitude of the resultant of two forces of constant magnitude is F and G. When the forces act at an angle 2α, the resultant in magnitudes is equal to

1) √F2 cos2 ɑ + G2 sin2 ɑ 2) √F2 sin ɑ + G2 cos2 ɑ 3) √F2 + G2 4) √F2 - G2 Solution: (1) √F2 cos2 ɑ + G2 sin2 ɑ Let the forces are A and B,... View Article

The resultant of two equal forces is equal to either of these forces. The angle between them is

1) π / 4 2) π / 3 3) π / 2 4) 2π / 3 Solution: (4) 2π / 3 Let each of 2 equal forces be of magnitude P and let them be inclined at angle ɑ.... View Article

A force is resolved into components P and Q equally inclined to it. Then,

1) P = 2Q 2) 2P = Q 3) P = Q 4) None of these Solution: (3) P = Q It is a fact.... View Article

The maximum resultant of two forces is P and the minimum resultant is Q, the two forces are at right angles, the resultant is

1) P + Q 2) P – Q 3) (1 / 2) √P2 + Q2 4) √[P2 + Q2] / 2 Solution: (4) √[P2 + Q2] / 2 Let the 2 forces be F1 and F2. Maximum resultant = P =... View Article

The resultant of two forces 3P and 2P is R, if the first force is doubled, the resultant is also doubled. The angle between the forces is

1) π / 3 2) 2π / 3 3) π / 6 4) 5π / 6 Solution: (2) 2π / 3 The two forces are 3p and 2p. Assume the angle between two forces to be θ.... View Article

When the origin is changed, then the coefficient of correlation

1) becomes zero 2) varies 3) remains fixed 4) None of these Solution: (3) remains fixed The value of the coefficient of correlation is... View Article

If there exists a linear statistical relationship between two variables x and y, then the regression coefficients of y on x is

1) cov (x, y) / 𝜎 x 𝜎y 2) cov (x, y) / 𝜎 y2 3) cov (x, y) / 𝜎 x2 4) None of these Solution: (3) cov (x, y) / 𝜎 x2 The linear statistical... View Article