**1) A body is on the point of sliding down an inclined plance under its own weight. If the inclination of the plane to the horizon be , the angle of friction will be****a)** **b)** **c)** **d)**

**2) A body consists of a solid cylinder with radius a and height a together with a solid hemisphere of radius a placed on the base of the cylinder. The centre of gravity of the complete body is****a)** inside the cylinder**b)** inside the hemisphere**c)** On the interface between the two**d)** Outside both

**3) Two like parallel forces P and Q act on a right body at A and B respectively. If P and Q interchanged in position, show that the point application of the resultant will be displaced through a distance d along AB , where d=****a)** **b)** **c)** **d)**

**4) If the position of the resultant of two like parallel forces P and Q is unaltered, when the positions of P and Q are interchanged then****a)** P = Q**b)** P= 2Q**c)** 2P= Q**d)** None of these

**5) P and Q are like parallel forces, If P is moved parallel to itself through a distance x, then the resultant of P and Q moves through a distance****a)** **b)** **c)** **d)** None of these

**6) Two unlike parallel forces P and Q act at points 5 m apart, If the resultant force is 9 N and acts at a distance of 10 m from the greater force P, then ****a)** P=16 N, Q= 7N**b)** P= 15 N, Q= 6 N**c)** P=27 N, Q= 18 N**d)** P= 18 N, Q= 9N

**7) **

**If the resultant of two like parallel forces of magnitudes 6N and 4 N acts at a distance of 12 cm from the line of action of the smaller force, then the distance between the lines of action of the forces is**

**a)**18 cm

**b)**24 cm

**c)**20 cm

**d)**none of these

**8) **

**If the resultant of two unlike parallel forces of magnitudes 10 N and 16 N act along a line at a distance of 24 cm from the line of action of the smaller force, then the distance between the lines of action of the forces is**

**a)**12 cm

**b)**8 cm

**c)**9 cm

**d)**18 cm

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

**10) If two like parallel forces of and have a resultant of 2 Newtons, then ****a)** P = Q**b)** P= 2Q**c)** 2P=Q**d)** None of these

**11) If R and R’ are the resultant of two forces and according as they are like or unlike such that R:R’=25:7, then P:Q = ****a)** 2:1**b)** 3:4**c)** 4:3**d)** 1:2

**12) **

**The resultant of two parallel forces P,Q acting at A and B respectively acts at C when like and D when unlike . If P>Q then CD=**

**a)**

**b)**

**c)**

**d)**None of these

**13) The resultant of two like parallel P, Q passes through a point O. If the resultant also passes through O when Q and R replace P and Q respectively, then****a)** P, Q, R in GP**b)** Q, P, R are in GP**c)** R, P, Q are in GP**d)** P,Q,R are in GP

**14) If each of the two unlike parallel forces P and Q (P>Q) acting at a distance d apart be increased by S, then the point of application of the resultant is moved through a distance****a)** **b)** **c)** **d)**

**15) Three parallel forces P, Q, R act at three points A, B, C of a rod at distance of 2 m, 8 m and 6 m respectively from one end. If the rod be in equilibrium, then P : Q : R = ****a)** 1:2:3**b)** 2:3:1**c)** 3:2:1**d)** None of these

**16) **

Two like parallel forces of 5 N and 15 N, act on a light rod at two points A and B respectively 6 m apart. The resultant force and the distance of its point of application from the point A are

**a)**10 N, 4.5 m

**b)**20 N, 4.5 m

**c)**20 N, 1.5 m

**d)**10 N, 1.5 m

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

**18) Three like parallel forces P, Q, R act at the corner points 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

**19) If the angle between two forces of equal magnitude is reduced to then the magnitude of their resultant becomes times of the earlier one. The angle is****a)** **b)** **c)** **d)**

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

**21) The resultant of P and Q is R. If P is reversed Q remaining the same, the resultant becomes. If R is perpendicular to , then****a)** **b)** **c)** **d)** None of these

**22) The resultant of P and Q is R. If Q is doubled, R is also doubled and if Q is reversed, R is again doubled. The P : Q : R is given by****a)** **b)** **c)** **d)**

**23) If the greatest and the least resultants of two forces are P and Q, respectively, then the resultant of these forces, when acting at right angles, will be****a)** **b)** **c)** **d)**

**24) 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)**

**25) The sum of two forces is 18 and their resultant is 12, which is perpendicular to the smaller force. Then the smaller force is****a)** 3**b)** 7**c)** 5**d)** 15

**26) If forces of magnitudes P, Q and R act at a point parallel to the sides BC, CA and AB respectively of a triangle ABC. The magnitude of their resultant is****a)** **b)** **c)** **d)** None of these

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

**28) Forces 7, 5 and 3 acting on a particle are in equilibrium. The angle between the last pair of forces is****a)** **b)** **c)** **d)**

**29) Forces of 1 and 2 units act along the lines x=0, y=0. The equation of the line of action of the resultant is****a)** **b)** **c)** **d)**

**30) Two like parallel forces 5N and 15N, act on a light rod at two points A and B respectively, 6 m apart. The resultant force and the distance of its point of action from the point A are****a)** **b)** **c)** **d)**

**31) P and Q (P>Q) are like parallel forces. If P is moved parallel to itself through a distance x, then the resultant of P and Q moves through a distance****a)** **b)** **c)** **d)** None of these

**32) If the forces 6W, 5W acting at a point (2,3) in Cartesian rectangular coordinates are parallel to the positive x and y axis respectively, then the moments of the resultant force about the origin is****a)** **b)** **c)** **d)**

**33) A horizontal rod AB is suspended at its ends by two vertical strings. The rod is of length 0.6 metre and weights 3 units. Its center of gravity G is at a distance 0.4 metre from A. Then the tension of the string at A, in the same unit, is****a)** 0.2**b)** 1.4**c)** 0.8**d)** 1.0

**34) Two weights of 10 gms and 2 gms hang from the ends of a uniform lever one meter long and weighting 4 gms. The point in the lever about which it will balance is from the weight of 10 gms. At a distance of****a)** 5 cm**b)** 25 cm**c)** 45 cm**d)** 65 cm

**35) A light rod AB of length 30 cm. Rests on two pegs 15cm apart. At what distance from the end A the pegs should be placed so that the reactions of pegs may be equal when weights 5 W and 3 W are suspended from A and B respectively?****a)** 1.75 cm, 15.75 cm**b)** 2.75 cm, 17.75 cm**c)** 3.75 cm, 18.75 cm**d)** None of alone

**36) A blacksmith carries a hammer on his shoulder and holds it at the other end of its light handle in his hand. If he changes the point of support of the handle at the shoulder and if x is the distance between his hand and the point of support, then the pressure on his shoulder is proportional to****a)** **b)** **c)** **d)**

**37) At what height from the base of a vertical pillar, a string of length 6 mt be tied, so that a man sitting on the ground and pulling the other end of the string has to apply minimum force to overturn the pillar ?****a)** **b)** **c)** **d)**

**38) Three like parallel forces P, Q, R act at the corners of a Their resultant passes through the incentre of the triangle then P : Q : R =****a)** **b)** **c)** **d)** None of these

**39) The resultant of forces P, Q, R acting along the sides BC, CA, AB of a triangle ABC passes through its circumcentre. Then****a)** **b)** **c)** **d)**

**40) A force units act along the line the moment of the force about the point (4,1) along z-axis is****a)** 0**b)** **c)** 5**d)** none of these

**41) A string ABC has its extremities tied to two fixed points A and B in the same horizontal line. If a weight W is knotted at a given point C, then the tension in the portion CA is (where a, b, c and the sides and is the area of triangle ABC)****a)** **b)** **c)** **d)**

**42) A rod can turn freely about one of its ends which is fixed. At the other end a horizontal force equal to half the weight of the rod is acting. In the position of equilibrium, the rod is inclined to the vertical at an angle****a)** **b)** **c)** **d)** None of these

**43) A uniform rod length 15 cm is suspended from a fixed point by two strings of lengths 9 cm and 12 cm attached at its ends. If the inclination of the rod to the vertical is then ****a)** **b)** **c)** **d)** None of these

**44) A uniform rod BC of length 6 cm and weight 2 kg can turn freely about the fixed point B. The rod is attached to the point A by a string AC of length 8 cm. The points A and B are in a horizontal line at a distance 10 cm. The tension in the string is****a)** **b)** **c)** **d)** None of these

**45) The resultant of two forces sec B and sec C along sides AB, AC of a triangle ABC is a force acting along AD when D is****a)** **b)** **c)** **d)**

**46) A body of mass 10 kg is suspended by two strings 7 cm and 24 cm long, their other ends being fastened to the extremities of a rod of length 25 cm. If the rod be so held that the body hangs immediately below its middle point, then the tension of the strings in kg. wt. are****a)** **b)** **c)** **d)** None of these

**47) Two forces P and Q acting parallel to the length and base of an inclined plane respectively would each of them singly support a weight W, on the plane, then ****a)** **b)** **c)** **d)** None of these

**48) A sphere of radius r and weight W rests against a smooth vertical wall, to which is attached a string of length l where are end is fastened to a point on the wall and the other to the surface of the sphere. Then the tension in the string is****a)** **b)** **c)** **d)** None of these

**49) A bead of weight W can slide on a smooth circular wire in a vertical plane, the bead is attached by a light thread to the highest point of the wire, and in equilibrium the thread is taut. Then the tension of the thread and the reaction of the wire on the bead, if the length of the string is equal to the radius of the wire, are****a)** **b)** **c)** **d)** None of these

**50) A uniform rod AB of length a hangs with one end against a smooth vertical wall, being supported by a string of length l, attached to the other end of the rod and to a point of the wall vertically above B. If the rod rests inclined to the wall at an angle, then ****a)** **b)** **c)** **d)** None of these

**51) A body is in equilibrium an a rough inclined plane of which the coefficient of friction is . The angle of inclination of the plane is gradually increased. The body will be on the point of sliding downwards when the inclination of the plane reaches****a)** **b)** **c)** **d)**

**52) A body of weight 40 kg rests on a rough horizontal plane, whose coefficient of friction is 0.25. The least force which acting horizontally would move the body is****a)** 10 Kg wt**b)** 20 Kg wt**c)** 30 Kg wt**d)** 40 Kg wt

**53) The foot of an uniform ladder is on a rough horizontal ground and the top rests against a smooth vertical wall. The weight of the ladder is 400 units A man weighting 800 units stands on the ladder one quarter of its length from the bottom, If the inclination of the ladder to the horizontal is , the reaction at the wall is****a)** 0**b)** **c)** **d)**

**54) A uniform ladder rests in limiting equilibrium, its lower end on a rough horizontal plane and its upper end against a smooth vertical wall. If is the angle of inclination of the ladder to the vertical wall andis the coefficient of friction, then tan is equal to****a)** **b)** **c)** **d)**

**55) A rough inclined plane has its angle of inclination equal to and =0.5. The magnitude of the least force in kg wt parallel to the plane required to move a body of 4 kg up the plane is****a)** **b)** **c)** **d)**

**56) The end of a heavy uniform rod AB can slide along a rough horizontal rod AC to which it is attached by a ring. B and C are joined by a string. If be a right angle, when the rod is on the point of sliding , the coefficient of friction and the angle between AB and the vertical, then****a)** **b)** **c)** **d)**

**57) A hemi spherical shell rests on a rough inclined plane, whose angle of friction is the inclination of the plane base of the rim to the horizon cannot be greater than****a)** **b)** **c)** **d)**

**58) A solid cone of semi-vertical angle is placed on a rough inclined plane. If the inclination of the plane is increased slowly and tan, then****a)** cone will slide down before toppling**b)** cone will topple before sliding down**c)** cone will slide and topple simultaneously**d)** cone will rest in limiting equilibrium

**59) A circular cylinder of the radius r and height h rests on a rough horizontal plane with one of its flat ends on the plane. A gradually increasing horizontal force is applied through the center of the upper end. If the coefficient of friction is ,the cylinder will topple before sliding, if****a)** **b)** **c)** **d)**

**60) 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 center of the forces is at the****a)** Centroid**b)** Circum-centre**c)** In-centre**d)** None of these

**61) Weights 2,3,4 and 5 lbs are suspended from a uniform lever 6 ft long at distances of 1,2,3 and 4 ft from one end. If the weight of the lever is 11 lbs, then the distance of the point at which it will balance from this end is****a)** 53/25**b)** 63/25**c)** 73/25**d)** None of these

**62) In a right angled triangle one side is thrice the other side in length. The is suspended by a string attached at the right angle. The angle that the hypotenuse of the will make with the vertical is****a)** **b)** **c)** **d)** None of these

**63) A solid right circular cylinder is attached to a hemisphere of equal base. If the C.G. of the combined solid is at the center of the base, then the ratio of the radius and height of the cylinder is****a)** 1:2**b)** **c)** 1:3**d)** None of these

**64) ABC is a uniform triangular lamina with center of gravity G. If the portion GBC is removed the center of gravity of the remaining portion is at G’. Then GG’ is equal to****a)** **b)** **c)** **d)**

**65) If the sum of the resolved parts of a system of coplanar forces along two mutually perpendicular direction is zero, then the sum of the moment of the forces about a given point is****a)** is zero always**b)** is positive always**c)** is negative always**d)** may have any value

**66) 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

**67) Two parallel forces not having the same line of action form a couple if they are****a)** like and unlike**b)** like and equal**c)** unequal and unlike**d)** none of these

**68) Three forces P, Q, R act along the sides BC, AC and BA of an equilateral triangle ABC. If their resultant is a force parallel to BC through the centroid of the triangle ABC, then****a)** P = Q= R**b)** P = 2Q = 2R**c)** 2P = Q +2R**d)** 2P = 2Q =R

**69) Three forces P,Q,R act along the sides BC, CA, AB of a triangle ABC, taken in order, if their resultant passes through the incentre of , then ****a)** **b)** **c)** **d)** None of these

**70) Three forces P,Q,R act along the sides BC,CA,AB of a taken in order, if their resultant passes through the centroid of , then****a)** P + Q + R = 0**b)** **c)** **d)** None of these

**71) 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

**72) Forces forming a couple are of magnitude 12 N each and the arm of the couple is 8 m. The force of an equivalent couple whose arm is 6m is of magnitude****a)** 8 N**b)** 16 N**c)** 12 N**d)** 4 N

**73) 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

**74) Two unlike parallel forces acting at points A and B form a couple of moment G. If their lines of action are turned through a right angle, they form a couple of moment H. Show that when both act at right angles to AB, they form a couple of moment****a)** **b)** **c)** **d)** none of these

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

**76) The forces represented in magnitude directions and position by sides of a triangle taken in order****a)** are in equilibrium**b)** form a couple**c)** are reducible to a single force**d)** form a couple

**77) The resultant of two unlike parallel forces of magnitudes P each acting at a distance of p is a****a)** force P**b)** couple of moment p.P**c)** force 2P**d)** none of these

**78) If the forces acting along the sides of a triangle Le, 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

**79) If the resultant forces P,Q,R acting along the sides BC, CA, AB of a 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

**80) A rod can turn freely about one of its ends which is fixed. At the other end a horizontal force equal to half the weight of the body is acting. In the position of equilibrium, the rod is inclined to the vertical at an angle****a)** **b)** **c)** **d)** None of these

**81) The resultant of the forces 4,3,4 and 3 units acting along the sides AB, BC, CD, DA of a square ABCD of side ‘a’ respectively is****a)** a force through the centre of the square**b)** A couple of moment 7a**c)** A null force**d)** None of these

**82) 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

**83) ABCD is a rectangle such that AB= CD = a and BC = DA = b forces P, P act along AD and CB and forces Q, Q act along AB and CD. The perpendicular distance between the resultant of forces P, Q at A and the resultant of forces P, Q at C is****a)** **b)** **c)** **d)**

**84) P, Q, r are the points on the sides BC, CA, AB of the triangle ABC such that BP:PC = CQ:QA = AR:RB = m:n. If denotes the area of the , then the forces reduce to a couple whose moment is **

**a)**

**b)**

**c)**

**d)**

**85) Any two coplanar couples of equal moments****a)** balance each other**b)** are equivalent**c)** need not be equivalent**d)** none of these

**86) Forces P, 3P, 2P and 5P act along the sides AB, BC,CD and DA of the square ABCD, If the resultant meets AD produced at the point E then AD: DE****a)** 1:2**b)** 1:3**c)** 1:4**d)** 1:5

**87) A horizontal rod AB is suspended at its ends by two vertical strings. The rod is of length 0.6 m and weights 3 Newton’s. Its centre of gravity G is at a distance 0.4 m from a. Then the tension of the string at A is****a)** 0.2 N**b)** 1.4 N**c)** 0.8 N**d)** 1 N

**88) Forces of magnitudes 3, P, 5,10 and Q Newton’s are respectively acting along the sides AB, BC, CD, AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. If the resultant is a single force acting the other diagonal BD, then****a)** **b)** **c)** **d)** None of these

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

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

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

**92) If 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

**93) A heavy uniform rod 15cm long, is suspended from a fixed point by fastened to its ends, their lengths being 9 and 12 cm. If be the angle which the rod is inclined to the vertical , them ****a)** **b)** **c)** **d)**

**94) A light string of length l is fastened to two points A and b at the same level at a distance ‘a’ apart. A ring of weight W can slide on the string, and a horizontal force P is applied to it such that the ring is in equilibrium below B. the tension in the string is equal to****a)** **b)** law**c)** **d)**

**95) A uniform rod AB movable about a hinge at A rests with one end in contact with a smooth wall. If be the inclination of the rod to the horizontal , then reaction at the hinge is**

**a)**

**b)**

**c)**

**d)**None of these

**96) A uniform rod AB, 17 m long whose mass in 120 Kg rests with one end against a smooth vertical wall and the other end on a smooth horizontal floor, this end being tied by a chord 8 m long, to a peg at a bottom of the wall, then the tension of the chord is****a)** 32 Kg wt**b)** 16 Kg wt**c)** 64 Kg wt**d)** 8 Kg wt

**97) Three forces are acting at a point in a plane. The angles between and and and are and respectively, then for equilibrium forces, P, Q, R are in the ratio****a)** **b)** **c)** **d)**

**98) Forces perpendicular to AB, BC and 2 CA act along the sides of in order. Then their resultant is represented by****a)** **b)** **c)** **d)**

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

**100) D and E are the mid-points of the sides AB and AC respectively of a . The resultant of the forces is represented by and is****a)** **b)** **c)** **d)**

**Answers**