Leadstar Academy Physics Past Paper PDF 2016/2024

**Leadstar Academy** **SUPLIMENTARY QUESTIONS FOR GRADE 12** **FOR THE PURPOSE OF PREPARATION OF UEE 2016/2024** **PHYSICS PART II. DYNAMICS AND ROTATION OF REGID BODY** 1. A force applied to a rocket gives it an acceleration equal to 2g. ( Note that g stands for acceleration due to gravity...

**Leadstar Academy** **SUPLIMENTARY QUESTIONS FOR GRADE 12** **FOR THE PURPOSE OF PREPARATION OF UEE 2016/2024** **PHYSICS PART II. DYNAMICS AND ROTATION OF REGID BODY** 1. A force applied to a rocket gives it an acceleration equal to 2g. ( Note that g stands for acceleration due to gravity ). The same force applied to a second rocket equal to 8g. Compare the mass of the two rockets. ANSWER ;- M~1~ = 4M~2~ 2. When a certain braking force is applied to a car moving at a given speed. The car is brought to rest in 10 seconds. A) if the braking force is doubled , what happens to the negative acceleration given to the car ? b) how long does it take the car to stop ? ANSWER:- a) a~2~ = 2a~1~ b) t~2~ = 2 second 3. An elevator whose mass is 200kgaccelerated down ward at 4.8m/s^2^. If the tension in the cable is 8000N , how many 70kg men are inside the elevator? ANSWER;- 19 men 4. A person stands on a scale in an elevator. The maximum and minimum scale readings are 591 and 391N , respectively. Assume the magnitude of the acceleration is the same during starting or stopping. Determine:- a) the weight of a person b) the person's mass c) the acceleration of the elevator. ANSWER:- a) 491N b) 49.1kg c) 2.04m/s^2^ 5. A 0.5 kg trolley is on top of a frictionless table. A thread tied to the trolley passes over a frictionless pulley and then attached to a 1kg block. What is :- a) the tension in the thread b) the acceleration of the trolley c) the acceleration of the block. ANSWER:- a) 3.3N b) 6.67m/s^2^ c) 6.67m/s^2^ 6. A horse that weighs 250kg changes its speed from 8m/s to 12m/s in 2 seconds in its initial run. The coefficient of friction between the hoofs and the ground is 0.3 a) what is the accelerating force of the horse b) what is the force if a 70kg man is on the back of the horse c) what is the internal force of the horse in (a) and ( b). ANSWER:- a) 500N b) 640N c) i) 1250N ii) 1600N 7. A 5kg block on a table to which µ = 0.4 is connected to a knot K by a horizontal string. Another block hangs from point K and a string makes 60^o^ from the vertical wall in which the string is fixed. What is the tension T~1~ , T~2~ and T~3~ and the maximum mass (m~3~) of the suspended block before the 5kg starts to slide. ANSWER:- a) T1 = 20N T2 = 22.6 N T3 = 11.3 N m = 1.13kg 8. A light horizontal wire is stretched between two posts 20m apart. A bird of 2kg slights at the center of the wire and the wire sags 10m. What is the tension in the wire when the bird is sitting on it. ANSWER:- T~1~ = 14.2 N T~2~ = 14.2 N 9. A string attached to m1 passes over two frictionless and mass less pulleys and is then attached to a rigid support as shown in the figure. There is no friction between the block with mass m1 and the horizontal table top. In terms of m1 , m2 and g , find the acceleration of each block. ANSWER: - T~1~ = m~1~a~1~ , T~2~ = 4m~1~a~2~ a~2~ = m~2~g/4m~1~ + m~2~ , a~1~ = 2m~2~g/4m~1~ + m~2~ 10. An 80kg man stands on a scale in an elevator. What is the apparent weight of the man if the elevator is a) at rest B) moving upward with a constant speed of 15m/s c) moving with an upward acceleration of 2m/s^2^ d) moving with a downward acceleration of 3m/s^2^. ANSWER:- a) 800N b) 800N c) 1600N d) 560N 11. In the figure shown below assume all surfaces are friction less and the pulley is mass less, F = 15N , m~1~ = 10kg , m~2~ = 20kg. Compute the acceleration of m~1~ and m~2~ and the tension in the string. Answer:- a~1~ = 0.5 m/s^2^ , a~2~ = 0.25 m/s^2^ , T = 5N 12. In figure below , m~1~ = 2kg ,m~2~ = 8kg and the coefficient of friction between all surfaces is 0.25. Find the magnitude of the horizontal force F necessary to drag m~2~ to the left at constant speed if m~1~ and m~2~ are connected by a light , flexible cord passing around a fixed friction less pulley. Answer:- 35N. 13. Two masses m~1~ = 10kg , m~2~ = 15kg are sliding down are inclined plane of angle θ = 37^o^ with friction as shown below. Find a) the force of interaction ( action -- reaction pair ) between the masses. b) the acceleration of the masses. ANSWER:- a) 7.2N b) 4.72 m.s^2^ 14. Two blocks m~1~ and m~2~ are placed as in the figure below, and connected by a ropes of negligible mass to block m~3~. Both m~1~ and m~2~ weighs 30N each and the coefficient of friction between each block and the surface is 0.4. The third block m~3~ descends with constant velocity. A) Find the tension in the rope connecting m~1~ and m~2~. b) what is the weight of m~3~ ? ANSWER:- a) T = 12N b) W = 39.6 N 15. For the system shown below , calculate the acceleration of m~1~ = 2kg and m~2~ = 3kg. Assume the pulley and the incline plane to be friction less. ANSWER:- a) a~1~ = 1.7m/s^2^ b) a~2~ = 0.85 m/s^2^ 16. The three blocks shown below are connected by mass less strings that passes over friction less pulleys. The acceleration of the system is 2.5 m/s^2^ to the left and the surface are rough. Find a) the coefficient of kinetic friction between blocks and surfaces b) the tension in the strings. Assume the same µ for both blocks. ANSWER:- a) µ = 0.82 b) T~1~ = 75 N , T~2~ = 21.5 N 17. Add the following forces by the component method F~1~ = 20N at 30^o^ to an X axis, F~2~ = 25N at 120^o^ at an X axis , F~3~ = 16N at an X axis ANSWER:- F~R~ = 21.93N 18. In arrangement shown below , the blocks A , B , C and D have masses m~1~ , m~2~ , m~3~ and m~4~ respectively. The springs are weight less and have force constant K and the string and pulley are light and smooth. The system is maintained in equilibrium by the thread DG connecting block D to the ground. If the thread is cut at a certain moment, determine the accelerations of the blocks immediately after wards. ANSWER:- a~4~ = ( m~1~+ m~2~ - m~3~ -- m ~4~) X g / m~4~. The other acceleration are not immediately affected. So , a~1~ = a~2~ = a~3~ =0 19. A body is moving along a straight line and its acceleration varies with time according to the equation , a = 2 -- 3 t. Five seconds after the motion was observed , its velocity is 20m/s. After another 5 seconds , it was 85m from the origin. Find its velocity, acceleration , distance of the body when it just stops, from the origin. ANSWER:- a) velocity = 47.5m/s b) a = 2m/s^2^ c) S = 10m and it stops when S = 223.94m. 20. The system shown in the figure below starts to accelerate from rest. A) how far does the block A move in 3.5 seconds if friction is ignored ? b) how could the solution of part ( a ) be changed if the coefficient of friction between the surface and the block is 0.4? ANSWER:- a) S = 50.75m b) S = 38.5 m 21. Based on the figure below , compute the acceleration and the tension in the string if the surface are :- a) friction less b) with coefficient of friction µ = 0.5 ANSWER:- a) a = 4.8m/s^2^ , T = 19.2 N b) a = 1m/s^2^ , T = 24 N 22. Three masses m1= 25kg , m2 = 10kg , m3 = 5kg are connected by light strings as shown in the figure below. Compute the acceleration and the tension in the strings if the :- a. Inclined plane is friction less b) coefficient of kinetic friction between m2 , m3 and the surface is 0.2. ANSWER:- a) a = 4m/s2 , T = 150 N b) a = 3.4m/s2 , T = 165 N 23. In the figure below when m~3~ = 3kg , the acceleration of the block m is 0.6 m/s^2^ , while a = 1.6 m/s^2^ if m = 4 kg. Find the friction force on block M as well as its mass. Neglect the mass and friction of the pulleys. ANSWER:- f = 12.48 N , M = 1.35 kg 24. A 6kg object has a velocity of 4 j m/s at one instant. 5 seconds later, its velocity is ( 6 i + 8 j ) m/s.Assuming the object was subject to a constant net force , find a. The components of the force b) its magnitude ANSWER:- a) F = ( 7.2 I + 4.8 j ) N b) F = 8.65 N 25. For the figure shown , determine the acceleration and the tension in the connecting cord. A) when friction is negligible b) when there is a coefficient of friction 0.2 , exists between the blocks and the surface. ANSWER:- a) a = 40/7 m/s^2^ , T = 240/7 N b. A = 34/7 m/s^2^ , T = 288/7 N 26. A block of mass 2kg is placed on a block of mass 4kg. The lower block is on a friction less horizontal surface and is subjected to a force of 30N. Find the minimum value of the coefficient of friction such that the 2kg mass does not slide on the 4kg mass. ANSWER:- µ = F/ (m~1~ + m~2~ ) g 27. For the system shown below , find the tension and acceleration a) if friction is neglected b) if the coefficient of friction between surface is 0.2 ANSWER :- a) a = 48/11 Mg b) T~1~ = 24.48/11 Mg T~2~ = 42.72/11 Mg 28. For the system shown in the figure, find the acceleration and the tension a) if no friction b) if there is a friction coefficient between the plane and the mass is 0.2. ANSWER:- a) a = 8/3 m/s^2^ , T = 26/3 m b) a = 1.6 m/s^2^ , T = 9.2 m ( here m=mass) 29. For the system shown in the figure ,find the acceleration , if the coefficient of friction between surfaces is µ ? ANSWER:- a = ( 8 -- 7 µ ) g/13 30. For the system shown in the figure , find the acceleration and the tension in the string. System is friction less. ANSWER:- a~1~ = 40/7 m/s^2^ , a~2~ = 20/7 m/s^2^ , a~3~ = 10/7 m/s^2^ , T~1~ = 80/7 N , T~2~ = 160/7 N 31. The two ends of a rope are fastened at two vertical poles that are 20 meters apart. If an object of weight 850 N hangs at the middle of the rope, the rope sags by 0.5m as shown below. Find the tension of the cord at each side when the object is suspended:- a) at the middle of the rope b) at the distance equal to three- fourth of the length of the rope from the left tie. ANSWER:- a) T = 8510.6 N b) T~1~ = 7355.05N, T~2~ = 7379.63N 32. In the figure below , six cords suspend an object of mass m , Find the tension across each cord and the weight of the block. If T~6~ = 20 N ANSWER:- T~2~ = T~3~ = 15 N , T~1~ = W = 24N , T~4~ = 7N , T~5~ = 20 N. 33. The mass m of the bl0ck that is tied to one end of a cord and placed on an inclined plane , is related to the mass M of the suspended one by m/M = 5. The fixed pulley at the top of the incline is frictionless. Find the angle θ , if the coefficient of friction between the block and the surface of the incline is :- a) Zero b) 0.2 ANSWER:- a) θ = 16^o^ b) θ = 27^o^ 34. If the weight of the suspended block shown in the figure below is 500 N , find T~1~ , T~2~ , T~3~ and T~4~. ANSWER:- T~1~ = 860 N T~2~ = 1000N T~3~ = 1447.4 N T~4~ = 1162.79 N 35. Two identical uniform ladders AB and AC ( as shown in the figure below ) each weighing 60 N are hinged at their heads ( at point A ). The hinge is 4m above the ground and the feet of the ladders are 8m apart. A light cord , tied at their centers , holds them together. Two objects of each weighing 100 N are suspended at positions indicated in the figure. A) compute the normal forces exerted on the ladders by the floor b) Find the tension in the cord. ANSWER:- a) V = 185 N , V' = 135 N. b) T = 170N 36. A uniform road of mass M and length L leans against a smooth vertical wall, making an angle θ1 with it as shown in the figure below. Its other end is supported by a smooth plane that makes an angle θ2 with the horizontal. Find a relation between θ1 and 2θ. ANSWER:- tan θ1 = 2 tan θ2. 37. The figure below represents a 2kg and 3kg objects connected by a horizontal weightless rod of length 6m. The system is pivoted at its center of mass. Find the distance of the center of mass of the system from the 2kg object. ANSWER:- r~1~ = 3.6 m 38. The tension through the tower guy wire , which is anchored by means of a bolt at point A. is 500 N. If OB = 40m, AE = AD = 10m, CD = 20m , then determine components F~x~ , F~y~ and F~z~ of the acting on the bolt. ANSWER :- F~x~ = - 1000N, F~y~ = 2000N, F~z~ = 500N 39. Two forces of magnitude 400N and 500 N are applied at the tie of the two cables , AO and OB as shown below. If α = 30^o^ , β = 60^o^ , and θ = 37^o^ , then determine tension in cables OA and OB. ANSWER :- T~A~ = 300 N , T~B~ = 174.42 N 40. A 16m long uniform plank of weight 100 N rests symmetrically on two supports that are 8m apart as shown below. A snake of length 0.8m and weight 200N starting from point P , slides to the right with a uniform velocity over the plank. The center of mass of the snake is at a distance of 0.2 m from its head. Let x be the instantaneous position of the CM of the snake with respect to point P. a. Find forces F~p~ and F~Q~, exerted by supports P and Q respectively , and express your answer as a function of x. b) Find the value of x from point p , at which the plank tips. C) How far from support P should support Q be placed so that the snake slides until its CM reaches just to the end of the plank without causing it to tip. ANSWER :- a) F~p~ = 250N -- ( 25 N/m ) x , F~Q~ = ( 25N/m ) x + 50N b) x = 10m c) x = 9.3m 41. A uniform beam of length 5m and mass 10kg support a block of mass 15kg as shown in the figure below. Determine the tension T in the supporting cord and the components. ( V and H ) of the reaction force at the hinge ( point P ). ANSWER :- T = 125 N , H= 75N 42. A uniform rod of length 8m is acted by four coplanar forces as shown below. If the rod remains stable, find forces F~2~ , F~4~ and the angle θ~z~. ANSWER:- F~2~ = 18.32 N , F~4~ = 13.5 N , θ~z~ = 40^o^ 43. A uniform rectangular block rests motionless on an inclined plane as shown below. The coefficient of static friction between the block and the surface of the incline is µ = 0.75 a) Compute the maximum angle θ that the inclined plane makes with the horizontal. b. Find the minimum value of the length L of the block. ANSWER:- a) θ = 37^o^ b) L = 3m 44. Determine the force ( F ) required to keep the blocks shown in the figure moving at a constant speed ; m~2~ to the right and m~1~ to the left. The masses m~1~ and m~2~ have weights of 5N and 10N respectively and the coefficient of kinetic friction is µ = 0.4. for all surfaces. Assume that the pulley is mass less and friction less , and the cord to be mass less as well. ANSWER:- F = 10N 45. A 10 kg box is attached to a 7kg box which rests on a 30^o^ incline. The coefficient of friction between each box and the surface is µ = 0.1. Find a) the rate of acceleration of the system. b) the tension in the rope. ANSWER:- a) 1.1.m/s^2^ b) T = 21 N 46. A 3kg block initially at rest is pulled along a level floor by a 25N force at that makes an angle of 37^o^ above the horizontal. If the coefficient of friction between the block and the surface is 0.4 , what is the speed of the block at t = 1.55 second. ANSWER:- V = 7m/s 47. A horizontal force P is exerted on a 20kg box in order to slide it up a 30^o^ incline. The friction force retarding the motion is 80N. How much must P be if the acceleration of the moving box is to be :- a) Zero b) 0.75m/s^2^. ANSWER:- a) P = 207.8N b) P=225.2N 48. Block of mass 5kg is pushed horizontally by the action of a 75 N force that makes an angle of 37^o^ to the horizontal as shown in the figure. Determine the:- a. magnitude of the friction force b) acceleration of the block c) speed and distance covered by the block at the end of 5 seconds. ANSWER:- a) f = 38N b) a = 4.4m/s^2^ c) S = 55m 49. Two masses m~2~ = 10kg and m~1~ = 15kg connected by a light string are pulled horizontally over a frictionless surface by a force of 150N that makes an angle of 37^o^ to the horizontal. compute the acceleration of the system and the tension in the string. ANSWER:- a = 2m/s^2^ , T = 60N 50. For the system shown in the figure , find the tensions and accelerations of the system. Neglect frictional effects. ANSWER:- a~1~ = 34m/s^2^ , a2 = 5.7m/s^2^ , T = 40M , T\' = 2T = 80M