**1) ABCD is quadrilateral. Forces represented by act on particle. The resultant of these forces is****a)** **b)** **c)** **d)**

**2) If forces acting at a point can be represented by the sides of a triangle taken in order then****a)** **b)** **c)** **d)**

**3) If forces of 12, 5 and 13 units weight balance at a point, two of them are inclined at****a)** **b)** **c)** **d)**

**4) A particle is acted upon by three forces. P, Q and R. It cannot be in equilibrium, If P:Q:R =****a)** 1:3:5**b)** 3:5:7**c)** 5:7:9**d)** 7:9:11

**5) Three forces P,Q, R acting on a particle are in equilibrium. If the angle between P and Q is double the angle between P and R, then P is equal to****a)** **b)** **c)** **d)**

**6) Two men carry a weight of 240 Newton’s between them by means of two ropes fixed to the weight. One rope is inclined at to the vertical and the other at . The tensions in the ropes are****a)** **b)** **c)** **d)** None of these

**7) Three forces keep a particle in equilibrium. One acts towards west, another towards north east and the third towards south. If the first be 5N, then other two are****a)** **b)** **c)** **d)** None of these

**8) O is the circumcentre of . If the forces P,Q and R acting along OA, OB and OC are in equilibrium, then P:Q:R is****a)** sin A: sin B : sin C**b)** cos A : cos B : cos C**c)** a cos A: b cos B: c cos C**d)** a sec A: b sec B : c sec C

**9) 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 . If F is just enough to keep P in equilibrium , then F=****a)** **b)** **c)** **d)**

**10) The resultant of two forces P and Q is equal to and makes an angle of with the direction of P then ****a)** 1 or 2**b)** 3 or 5**c)** 3 or 4**d)** 4 or 5

**11) Two equal forces act at a point. If the square of the magnitude of their resultant is three times the product of their magnitudes, the angle between the forces is****a)** **b)** **c)** **d)**

**12) The resultant of two forces P and Q is at right angles to P, the resultant of P and Q’ acting at the same angle is at right angles to Q’. Then****a)** P,Q,Q’ Then**b)** Q,P,Q’ are in GP**c)** P,Q’,Q are in G.P**d)** None of these

**13) The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at with the force of smaller magnitude, then their magnitudes are****a)** 3,15**b)** 4,14**c)** 5,13**d)** 6,12

**14) A force F is resolved into two components P and Q. If P be at angles to F and has the same magnitude as that of F, then the magnitude of Q is****a)** **b)** **c)** **d)**

**15) Forces of magnitudes P-Q, P and P+Q act at a point parallel to the sides of an equilateral triangle taken in order. The resultant of these forces is****a)** **b)** **c)** **d)**

**16) If the resultant of two forces of magnitudes of P and Q acts at a point at an angle of is Q, then is****a)** 1**b)** **c)** 2**d)** 4

**17) Three forces of magnitude 30, 60 and P acting at appoint are in equilibrium. If the angle between the first two is , the value of P is****a)** **b)** **c)** **d)**

**18) If the resultant of two forces 2 P and P is P, then the angle between them will be****a)** **b)** **c)** **d)**

**19) **

**Which one of the following is not a force?**

**a)**Tension

**b)**Attraction

**c)**Weight

**d)**Acceleration

**20) If P and Q are two forces perpendicular to each other, then their resultant is ****a)** **b)** **c)** **d)**

**21) ABCDE is a pentagon. Forces acting on a particle are represented in magnitude and direction by and . Their resultant is given by****a)** **b)** **c)** **d)**

**22) If the line of action of the resultant of two forces P and Q divides the angle between them in the ratio 1 : 2, then the magnitude of the resultant is**

**a)**

**b)**

**c)**

**d)**

**23) If forces of 12, 5 and 13 units weight balance at a point, two of them are inclined at ****a)** **b)** **c)** **d)**

**24) The resultant of two forces 3 P and 2 P is R. If the first force is doubled, the resultant is also doubled. Then the angle between the forces is****a)** **b)** **c)** **d)**

**25) Forces proportional to AB,BC and 2 CA act along the sides of IN ORDER. then their resultant is represented in magnitude and direction by****a)** **b)** **c)** **d)**

**26) A particle is acted upon by three forces P,Q and R. It cannot be in equilibrium, if ****a)** P : Q : R =1 : 3 : 5**b)** P : Q : R =3 : 5 : 7**c)** P : Q : R =5 : 7 : 9**d)** P : Q : R =7 : 9 : 11

**27) The resultant of two equal forces is equal to either of these forces. The angle between them is ****a)** **b)** **c)** **d)**

**28) The magnitude of two forces are 3,5 and the direction of the resultant is at right angles to that of the smaller forces. The ratio of the magnitude of the larger force and of the resultant is**

**a)**5 : 3

**b)**5 : 4

**c)**4 : 5

**d)**4 : 3

**29) 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****a)** 5**b)** 3**c)** 7**d)** 15

**30) The maximum resultant of two forces is P and the minimum resultant is Q, the two forces are at right angles, the resultant is****a)** P +Q**b)** P-Q**c)** **d)**

**31) The resultant of two forces and is of magnitude P. If the force is doubled remaining unaltered, the new resultant will be****a)** **b)** **c)** **d)**

**32) If forces acting at a point can be represented by the sides of a triangle taken in order, then****a)** **b)** **c)** **d)**

**33) Three like parallel forces P,Q, R act at the corners of a triangle ABC. Their resultant passes through the circumcentre if **

**a)**

**b)**P = Q =R

**c)**P + Q +R =0

**d)**none of these

**34) Two like parallel forces P and Q act on a rigid body at A and B respectively. If P and Q be interchanged in position, then the point of application of the resultant will be displaced through a distance (along AB)**

**a)**(P – Q) AB

**b)**(P + Q)AB

**c)**

**d)**

**35) The resultant of forces P, Q, R acting along the sides BC, CA, AB of a triangle ABC passes through its circumcentre. Then****a)** P sin A + Q sin B +R sin C = 0**b)** P cos A + Q cos B +R cos C = 0**c)** P sec A + Q sec B +R sec C = 0**d)** P tan A + Q tan B +R tan C = 0

**36) The resultant of forces 10 and acting at the points (1,0), (0,2) and (0,0) respectively is****a)** **b)** **c)** **d)**

**37) If the sum of the resolved part of a system of coplanar forces along two mutually perpendicular directions is zero, then the sum of moments of the forces about a given point is****a)** zero always**b)** positive always**c)** negative always**d)** any value

**38) Three forces P, Q, R act along the sides BC, CA, AB of a taken in order. If their resultant passes thro’ the incentre of , then****a)** **b)** P cos A + Q cos B +R cos C =0**c)** P + Q +R=0**d)** aP + bQ+ cR=0

**39) The moment of a system of coplanar forces (not in equilibrium) about three collinear points A,B,C in the plane are . Then****a)** **b)** **c)** **d)** none of these

**40) Like parallel forces act at the vertices A, B and C of a triangle and are proportional to the lengths BC,CA and AB respectively. The centre of the forces is at the****a)** centroid**b)** circum-centre**c)** in-centre**d)** none of these.

**41) The resultant of two unlike forces P and P at a distance pf p is a****a)** force P**b)** couple of moment p.P**c)** force 2 P**d)** force P/2

**42) If the forces acting along the sides of a triangle, taken in order are equivalent to a couple, then the forces are ****a)** equal**b)** proportional to sides of triangle**c)** in equilibrium**d)** in arithmetic progression

**43) A force units acts along the line . The moment of the force about the point (4,1) along x-axis is****a)** Zero**b)** **c)** **d)** -5

**44) A system of five forces whose directions and non-zero magnitudes can be chosen arbitrarily, will never be in equilibrium if n of the forces are concurrent where ****a)** n = 2**b)** n = 3**c)** n = 4**d)** n = 5

**45) A uniform beam of length 2a rests in equilibrium against a smooth vertical plane and over a smooth peg at a distance h from the plane. If be the inclination of the beam to the vertical, then is****a)** **b)** **c)** **d)**

**46) Let ABCD be a quadrilateral and O is any point within it. If and are in equilibrium, then****a)** O is mid pt. of AC**b)** O is the mid pt. of BD**c)** O is the mid point of each of the line segments joining the mid pts. of the opposite sides of quadrilateral ABCD**d)** None of these

**47) Three forces of the same magnitudes acting at a point are in equilibrium. If are the angles between every two, then are****a)** **b)** **c)** **d)** none of these

**48) A cubical block rests on inclined plane with four edges horizontal. The co efficient of friction is . the block just slides when the angle of the inclination of the plane is****a)** **b)** **c)** **d)**

**49) A body of weight 4 kg is kept on a plane inclined at an angle to the horizontal. It is in limiting equilibrium. The coefficient of friction is, then equal to****a)** **b)** **c)** **d)**

**50) The C.G. of three particles placed at the vertices of a triangle is****a)** the incentre**b)** the centroid**c)** the circumcentre**d)** the orthocentre

**51) The centre of mass of a rod of length ‘a’ cm, whose density varies as the square of the distance form one end, will be at a distance**

**a)**

**b)**

**c)**

**d)**

**52) A beam whose centre of gravity divides it into two portions a and b, is placed inside a smooth sphere. If q be its inclination to the horizon in the position of equilibrium and 2a be the angle subtended by the beam at the centre of the sphere, then****a)** tan q = (b-a) (b+a) tan a**b)** **c)** **d)**

**53) The resultant of two equal forces which act at an angle is times the resultant of same forces when acting at an angle , then****a)** cos a = 2 cos b;**b)** cos a = 3cos b**c)** 2cos a = 3cos b**d)** 3cos a; = 2cos b

**54) The sum of magnitude of two forces is 16 units. Their resultant acts at right angles to the smaller of the two forces and has magnitude of 8 units. The magnitude of the smaller force must be****a)** 6 units**b)** 8 units**c)** 10 units**d)** 12 units

**55) The law of parallelogram of forces gives****a)** only the direction of the resultant**b)** only the magnitude of the resultant**c)** both the magnitude and direction of the resultant**d)** None of these

**56) A body of weight W rests on a rough plane, whose coefficient of friction is m (= tan l ), which is inclined at an angle a with the horizon. Then the least force required to pull body up the plane is****a)** W sin(a – l )**b)** W win (a + l )**c)** W sin (l – a )**d)** W tan (a – l )

**57) The resultant of two forces P and Q is R. if Q is doubled, R is doubled and if Q is reversed, R is again doubled. If the ratio P ^{2}:Q^{2} :R^{2}=2:3:x then x is equal to**

**a)**5

**b)**4

**c)**3

**d)**2

**58) The resultant of two forces 3P and 2P is R, if first force is doubled, the resultant is also doubled. Then the angle between the forces is****a)** ^{}**b)** ^{}**c)** **d)**

**59) The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at with the force of smaller magnitude, then their magnitudes are****a)** 3,15**b)** 4,14**c)** 5,13**d)** 6,12

**60) Two concurrent forces are of magnitudes (P+Q) newtons and (P-Q) newtons. the angle between their line of action is , and their resultant is a force of 2 newtons, perpendiculat to the line of action of the second force. Then the values of P and Q are respectively****a)** **b)** **c)** **d)**

**61) Forces P and Q acting at a point O make an anglebetween them. their resultant acts at O, has magnitude 2 units and is perpendicular to P. then in the same unit, the magnitudes of P and Q are****a)** **b)** **c)** 3,4**d)** 4,5

**62) Forces proportional to AB, BC and 2 CA act along the sides of triangle ABC in order, their resultants represented in magnitude and direction is****a)** CA**b)** AC**c)** BC**d)** CB

**63) Two forces 13 kg weight and kg weight act on a particle at an angle and are equal to a resultant force of 14 kg weight, then the angle between the forces is****a)** **b)** **c)** **d)**

**64) R is the resultant of forces P and Q acting on a particle at O. If P is reversed, Q remaining the same, the resultant becomes R. If R and R are perpendicular to each other, then****a)** P =Q**b)** P =2Q**c)** 3P =Q**d)** None of these

**65) The greatest and least magnitudes of the resultant of two forces of constant magnitudes are F and G. When the forces act at an angle , the resultant in magnitude is equal to****a)** **b)** **c)** **d)**

**66) The directions of three forces 1 N, 2 N and 3 N acting at a point are parallel to the sides of equilateral triangle taken in order. The magnitude of theor resultant is****a)** 0**b)** **c)** **d)**

**67) Forces of magnitudes 3,4 and 5 Newton act at a point in direction parallel to the sides of an equilateral triangle taken in order. The magnitude of their resultant (in Newton) is****a)** **b)** 2**c)** **d)** 12

**68) Two equal forces act at a point. If the square of the magnitude of their resultant is three times the product of their magnitudes, the angle between the forces is****a)** **b)** **c)** **d)** none of these

**69) Two parallel forces not having the same line of action form a couple if they are****a)** like and unequal**b)** like and equal**c)** unequal and unlike**d)** equal and unlike

**70) A horizontal rod of length 5 m weight 4 kg is suspended at the ends by two strings. The weights 8 kg, 12 kg, 16 kg, and 20 kg are placed on the rod at distance 1m, 2m,3m and 4m from one end of the rod. Then the tensions in the string are****a)** 26,34kg.wt**b)** 20,30, kg.wt**c)** 10, 40 kg.wt**d)** None of these

**71) The resultant of two like parallel forces is 12 N. The distance between the forces is 18 metres. If one force is of 4 N, then the distance of the resultant from the smaller force is****a)** 4 m**b)** 8 m**c)** 12 m**d)** None of these

**72) The resultant of the forces 4,3,4 and 3 units acting along the lines AB, BC, CD, and DA of a square ABCD of side ‘a’ respectively is****a)** **b)** a couple of moment 7 a**c)** a null force**d)** none of these

**73) The resultant of non-parallel forces and a couple in a plane always reduces to****a)** a single force**b)** a couple**c)** Two forces**d)** None of these

**74) Two parallel forces not having the same line of action form a couple if they are****a)** like and unequal**b)** Like and equal**c)** Unequal and unlike**d)** Equal and unlike

**75) P and Q are two unlike parallel forces (P>Q). A couple of moment G is combined with them. Then the resultant is displaced thro’ a distance****a)** **b)** **c)** **d)**

**76) A body is in equilibrium under the action of three coplanar forces, then****a)** they must act in a straight line**b)** they must meet in a point**c)** their horizontal and vertical components are equal**d)** None of these

**77) The least force required to pull a body of weight W up an inclined rough plane is****a)** **b)** **c)** **d)**

**78) **

**The resultant of three equal like parallel forces acting at the vertices of a triangle act at its**

**a)**Incentre

**b)**Circumcentre

**c)**Orthocentre

**d)**Centroid

**79) **

**Three like parallel forces P, Q, R act at the corners A,B,C of a . If their resultant passes through the incentre of , then**

**a)**

**b)**

**c)**

**d)**

**80) The resultant of two equal forces in equal to either of these forces. The angle between them is****a)** **b)** **c)** **d)**

**81) If P and Q are forces perpendicular to each other, then their resultant is****a)** **b)** **c)** **d)**

**82) Three forces of magnitude 30,60 and P acting at a point are in equilibrium. If the angle between the first two is , the value of P is ****a)** **b)** **c)** **d)**

**83) If the resultant of two forces of magnitude P and 2P is perpendicular to P, then the angle between the forces is****a)** **b)** **c)** **d)**

**84) Forces M and N acting at a point O make an angle . Their resultant acts at O, has magnitude 2 units and is perpendicular to M. Then , in the same unit , the magnitude of M and N are ****a)** **b)** **c)** **d)**

**85) The resultant R of two forces P and Q act at right angles to P. then the angle between the forces is****a)** **b)** **c)** **d)**

**86) Two forces P and Q have a resultant R and the resolved part of R in the direction of P is of magnitude Q. then the angle between the forces is****a)** **b)** **c)** **d)** none of these

**87) When two equal forces are inclined at an angle , their resultant is twice as great as when they act at an angle , then****a)** **b)** **c)** **d)**

**88) The maximum resultant of two forces is P and the minimum resultant is Q, the two forces are at right angles, the resultant is****a)** P+Q**b)** P-Q**c)** **d)**

**89) The magnitudes of two forces are 3, 5 and the direction of the resultant is at right angles to that of the smaller force. The ratio of the magnitude of the larger force and of the resultant is****a)** 5:3**b)** 5:4**c)** 4:5**d)** 4:3

**90) 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****a)** 5**b)** 3**c)** 7**d)** 15

**91) If the line of action of the resultant of two forces P and Q divides the angle between them in the ratio 1:2, then the magnitude of the resultant is****a)** **b)** **c)** **d)**

**92) The resultant of two forces and is of magnitude P. If the force is doubled , remaining unaltered, the new resultant will be **

**a)**

**b)**

**c)**

**d)**

**93) The resultant of two forces 3P and 2P is R. If the first force is doubled, the resultant is also doubled. Then the angle between the forces is****a)** **b)** **c)** **d)**

**94) Two forces P and Q have a resultant R and the resolved part of R in the direction of P is of magnitude Q. Then the angle between the forces is****a)** **b)** **c)** **d)** none of these

**95) The resultant of three forces represented in magnitude and direction by the sides of a triangle ABC taken in order with BC = 5 cm, CA = 5 cm and AB = 8 cm, is a couple of moment****a)** 12 units**b)** 24 units**c)** 36 units**d)** 16 units

**96) Three forces P, Q, R acting at a point are in equilibrium. The angle between P and Q is , the angle between Q and R is and the angle between P and R is . Then the ratio P : Q : R is****a)** 2 : 3 : 4**b)** 1 : 2 : 3**c)** **d)** : 6

**97) The centre of gravity of a frustrum of a cone of height 15 cm, the ratio of the two ends being 5 cm and 10 cm is****a)** **b)** **c)** **d)** none of these

**98) The C. G. of the surface of a hollow cone lies on the axis and divides it in the ratio****a)** 1 : 2**b)** 1 : 3**c)** 2 : 3**d)** 1 : 1

**99) ****a)** tan 2x = 1**b)** tan 3 x = 1**c)**

tan^{2} x = 1

**d)**

tan^{3} x + 1

Answers