This is the Uncategorized Multiples Choice Questions Part 12 of the Series in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize each and every questions compiled here taken from various sources including past Board Exam Questions, Engineering Mathematics Books, Journals and other Engineering Mathematics References. In the actual board, you have to answer 100 items in Engineering Mathematics within 5 hours. You have to get at least 70% to pass the subject. Engineering Mathematics is 20% of the total 100% Board Rating along with Electronic Systems and Technologies (30%), General Engineering and Applied Sciences (20%) and Electronics Engineering (30%).

### The Series

Following is the list of multiple choice questions in this brand new series:

**Engineering Mathematics MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART 2**

**MCQs from Number 101 – 150**Answer key:

**PART 3**

**MCQs from Number 151 – 200**Answer key:

**PART 4**

**MCQs from Number 201 – 250**Answer key:

**PART 5**

**MCQs from Number 251 – 300**Answer key:

**PART 6**

**MCQs from Number 301 – 350**Answer key:

**PART 7**

**MCQs from Number 351 – 400**Answer key:

**PART 8**

**MCQs from Number 401 – 450**Answer key:

**PART 9**

**MCQs from Number 451 – 500**Answer key:

**PART 10**

**MCQs from Number 551 – 600**Answer key:

**PART 12**

### Continue Part XII of the Series

**Choose the letter of the best answer in each questions.**

551. A 10.7 kN car travelling at 134 m/s attempts to round an unbanked curve with a radius of 61 m. What force of friction is required to keep the car on its circular path?

- a. 3123 N
- b. 3445 N
- c. 3211 N
- d. 4434 N

552. A rotating wheel has a radius of 2 feet and 6 inches. A point on the rim of the wheel moves 30 ft. in 2sec. Find the angular velocity of the wheel.

- a. 2 rad/sec
- b. 4 rad/sec
- c. 5 rad/sec
- d. 6 rad/sec

553. A prismatic AB bar 6 m long has a weight of 500 N. It is pin connected at one end at A. If it is rotated about a vertical axis at Ai how fast would it be rotated when it makes an angle of 30° with the vertical?

- a. 1.68 rad/sec
- b. 2.58 rad/sec
- c. 1.22 rad/sec
- d. 2.21 rad/sec

554. A prismatic bar weighing 25 kg is rotated horizontally about one of its ends at a speed of 2.5 rad/sec. Compute the length of the prismatic bar when it makes an angle of 45° with the vertical.

- a. 6.5 m
- b. 3.33 m
- c. 6.20 m
- d. 7.35 m

555. A bullet enters a 50 mm plank with a speed of 600 m/s and leaves with a speed of 24 m/s. Determine the thickness of the plank that can be penetrated by the bullet.

- a. 55 mm
- b. 60 mm
- c. 65 mm
- d. 70 mm

556. A balikbayan box is placed on top on a flooring of a delivery truck with a coefficient of friction between the floor and the box equal to 0.40. If the truck moves at 60 kph, determine the distance that the truck will move before the box will stop slipping. The box weighs 200 N.

- a. 70.8 m
- b. 60.8 m
- c. 50.8 m
- d. 40.8 m

557. At what speed must a 10 kN car approach a ramp which makes an angle of 30° with the horizontal an 18 m high at the top such that it will just stop as it reaches the top. Assume resisting force of friction, to be 0.60 kN.

- a. 54.46 kph
- b. 60.46 kph
- c. 71.57 kph
- d. 82.52 kph

558. A car weighing 10 kN approaches a ramp which makes a slope of 20° at the speed of 75 kph. At the foot of the ramp, the motor is turned off. How far does the car travel up the inclined before it stops?

- a. 74.84 m
- b. 46.74 m
- c. 64.57 m
- d. 54.84 m

559. A car is running up a grade of 1 in 250 at a speed of 28.8 kph when the engine conk out. Neglecting friction, how far will the car have gone after 3 minutes from the point where the engine conk out?

- a. 808.2 m
- b. 607.8 m
- c. 542.4 m
- d. 486.8 m

560. A 70 kg man stands on a spring scale on an elevator. During the first 2 seconds starting from rest, the scale reads 80 kg. Find the velocity of the elevator at the end of 2 seconds and the tension T in the supporting cable fro the during the acceleration period. The total weight of the elevator, man and scale is 7000 N.

- a. 1.5 m/sec; 6000N
- b. 2.8 m/sec; 8000N
- c. 3.4 m/sec; 7000N
- d. 4.3 m/sec; 9000N

561. A cylinder having a mass of 40 kg with a radius of 0.5 m is pushed to the right without rotation and with acceleration 2 m/sec^2. Determine the magnitude and location of the horizontal force P if the coefficient of friction is 0.30.

- a. 183 N; 15.7 cm
- b. 200 N; 32.4 cm
- c. 198 N; 20.2 cm
- d. 232 N; 34.2 cm

562. A block having a weight of 400 N rests on an inclined plane making an angle of 30° with the horizontal is initially at rest. After it was released for 3sec, find the distance that the block has traveled assuming that there is no friction between the block and the plane. Compute also the velocity after 3 sec.

- a. 22.07 m, 14.71 m/s
- b. 27.39 m, 15.39 m/s
- c. 20.23 m, 14.60 m/s
- d. 15.69 m, 13.68 m/s

563. A block having a weight of 200 N rests on an inclined plane making an angle of 30° with the horizontal is initially at rest. If the block is initially at rest and the coefficient of friction between the inclined plane and the block is 0.20, compute the time to travel a distance of 14.45m, and the velocity of the block after 3 sec.

- a. 2 sec, 10.12 m/s
- b. 3 sec, 9.63 m/s
- c. 4 sec, 12.20 m/s
- d. 5sec, 11.20 m/s

564. A 100 kg block is released at the top of 30° incline 10 m above the ground. The slight melting of ice renders the surfaces frictionless; calculate the velocity of the foot of the incline.

- a. 25 m/s
- b. 15 m/s
- c. 20 m/s
- d. 22 m/s

565. Starting from rest, an elevator weighting 9000 N attains an upward velocity of 5 m/s in 4 sec. with uniform acceleration. Find the apparent weight of 600 N man standing inside the elevator during its ascent and calculate the tension in the supporting cable.

- a. 10 823 N
- b. 11 382 N
- c. 9 254 N
- d. 12 483 N

566. A body weighing 40 lb. starts from rest and slides down a plane at an angle of 30° with the horizontal for which the coefficient of friction f = 0.30. How far will it move during the third second?

- a. 19.63 ft
- b. 19.33 ft
- c. 18.33 ft
- d. 19.99 ft

567. What force is necessary to accelerate a 3000 lbs railway electric car at the rate of 1.25 ft/sec^2, if the force required to overcome the frictional resistance is 400 lbs.

- a. 1267.328 lbs
- b. 1427.937 lbs
- c. 1564.596 lbs
- d. 1653.397 lbs

568. A freight car having a mass of 15 Mg is towed along the horizontal track. If the car starts from rest and attains a speed of 8 m/s after traveling a distance of 150 m, determine the constant horizontal towing force applied to the car. Neglect friction and the mass of the wheels.

- a. 2.2 kN
- b. 3.2 kN
- c. 4.3 kN
- d. 4.1 kN

569. An elevator weighing 2000 lb attains an upward velocity of 16 fps in 4 sec with uniform acceleration. What is the tension in supporting cables?

- a. 1950 lb
- b. 2495 lb
- c. 2250 lb
- d. 2150 lb

570. A block weighing 200 N rests on a plane inclined upward to the right at slope 4 vertical to 3 horizontal. The block is connected by a cable initially parallel to the plane passing through a pulley which is connected to another block weighing 100 N moving vertically. The coefficient of kinetic friction between the 200 N block and the inclined plane is 0.10, which of the following most nearly give the acceleration of the system.

- a. 2.93 m/sec^2
- b. 0.37 m/sec^2
- c. 1.57 m/sec^2
- d. 3.74 m/sec^2

571. A pick-up truck is traveling forward a 5 m/s the bed is loaded with boxes, whose coefficient of friction with the bed is 0.4. What is the shortest time that the truck can be bought to a stop such that the boxes do not shift?

- a. 4.75
- b. 2.35
- c. 5.45
- d. 6.37

572. Two barges are weighing 40 kN and the other 80 kN are connected by a cable in quiet water. Initially the barges are 100 m apart. If friction is negligible calculate the distance moved by the 80 kN barge.

- a. 12 m
- b. 20 m
- c. 30 m
- d. 25 m

573. Two blocks A and B weighs 150 N and 200 N respectively is supported by a flexible cord which passes through a frictionless pulley which is supported by a rod attached to a ceiling. Neglecting the mass and friction of the pulley, compute the acceleration on the blocks and the tension on the rod supporting the frictionless pulley.

- a. 1.40 m/s^2, 342.92 N
- b. 1.50 m/s^2, 386.45 N
- c. 1.80 m/s^2, 421.42 N
- d. 2.2 m/s^2, 510.62 N

574. A pendulum with the concentrated mass “m” is suspended vertically inside a stationary railroad freight car by means of a rigid weightless connecting rod. If the connecting rod is pivoted where it attaches to the boxcar, compute the angle of that the rod makes with the vertical as a result of constant horizontal acceleration of 2 m/s.

- a. 11°31’
- b. 9°12’
- c. 6°32’
- d. 3°56’

575. Two 15 N weights A and B are connected by a massless string hanging over a smooth frictionless peg. If a third weight of 15N is added to A and the system is released, by how much is the force on the peg increased?

- a. 10 kN
- b. 12 kN
- c. 15 kN
- d. 20 kN

576. Three crates with masses A = 45.2 kg, B = 22.8 kg, and C = 34.3 kg are placed with B besides A and C besides B along a horizontal frictionless surface. Find the force exerted by B and C by pushing to the right with an acceleration of 1.32 m/s^2.

- a. 38.7 kN
- b. 43.2 kN
- c. 45.3 kN
- d. 54.2 kN

577. Three blocks A, B and C are placed on a horizontal frictionless surface and are connected by chords between A, B and C. Determine the tension between block B and C when a horizontal tensile force is applied at C = 6.5 N. Masses of blocks are A = 1.2 kg, B 2.4 kg, and C = 3.1 kg.

- a. 3.50 N
- b. 4.21 N
- c. 3.89 N
- d. 4.65 N

578. A constant force P = 750 N acts on the body shown during only the first 6 m of its motion starting from rest. If u = 0.20, find the velocity of the body after it has moved a total distance of 9m.

- a. 2.32 m/s^2
- b. 4.73 m/s^2
- c. 3.93 m/s^2
- d. 3.11 m/s^2

579. A weight 9 kN is initially suspended on a 150 m long cable. The cable weighs 0.002 kN/m. If the weight is then raised 100 m how much work is done in Joules.

- a. 905100
- b. 915000
- c. 951000
- d. 938700

580. What is the kinetic energy of 4000 lb. automobile which is moving at 44 fps?

- a. 1.2 x 10^5 ft-lb
- b. 2.1 x 10^5 ft-lb
- c. 1.8 x 10^5 ft-lb
- d. 3.1 x 10^5 ft-lb

581. A box slides from rest from a point A down a plane inclined 30° to the horizontal. After reaching the bottom of the plane, the box move at horizontal floor at distance 2m before coming to rest. If the coefficient of friction between the box and the plane and the box and the floor is 0.40, what is the distance of point “A” from the intersection of the plane and the floor?

- a. 7.24 m
- b. 5.21 m
- c. 4.75 m
- d. 9.52 m

582. A 400 N block slides on the horizontal plane by applying a horizontal force of 200 N and reaches a velocity of 20 m/s in a distance of 30m from rest. Compute the coefficient of friction between the floor and the block.

- a. 0.18
- b. 0.24
- c. 0.31
- d. 0.40

583. A car weighing 40 tons is switched to a 2 percent of upgrade with a velocity of 30 mph. If the train resistance is 10 lb/ton, how far up the grade will it go?

- a. 1124 ft on slope
- b. 2014 ft on slope
- c. 1203 ft on slope
- d. 1402 ft on slope

584. A car weighing 10 kN is towed along a horizontal surface at a uniform velocity of 80 kph. The towing cable is parallel with the road surface. When the car is at foot of an incline as shown having an elevation of 30 m, the towing cable was suddenly cut. At what elevation in the inclined road will the car stop in its upward motion?

- a. 49.62 m
- b. 60.24 m
- c. 51.43 m
- d. 55.16 m

585. A wooden block starting from rest, slides 6 m down a 45° slope, then 3 m along the level surface and then up 30° incline until it come to rest again. If the coefficient of friction is 0.15 for all surfaces in contact compute the total distance traveled.

- a. 20 m
- b. 11 m
- c. 14 m
- d. 18 m

586. The block shown starting from rest and moves towards the right. What is the velocity of block B as it touches the ground? How far will block A travel if the coefficient of friction between block A and the surface is 0.20? Assume pulley to be frictionless.

- a. 1.44 m
- b. 2.55 m
- c. 5.22 m
- d. 3.25 m

587. After the block in the figure has moved 3 m from rest the constant force P = 600N is removed find the velocity of the block when it is returned to its initial position.

- a. 8.6 m/s
- b. 5.6 m/s
- c. 6.4 m/s
- d. 7.1 m/s

588. A 10 kg block is raised vertically 3 meters. What is the change in potential energy? Answer in SI units closest to:

- a. 350 kg-m^2/ s
- b. 320 J
- c. 350N-m
- d. 294 J

589. A car weighing 40 tons is switched 2% upgrade with a velocity of 30 mph. If the car is allowed to run back what velocity will it have at the foot of the grade?

- a. 37 fps
- b. 31 fps
- c. 43 fps
- d. 34 fps

590. A 200 ton train is accelerated from rest to a velocity of 30 miles per hour on a level track. How much useful work was done?

- a. 10 287 846
- b. 11 038 738
- c. 12 024 845
- d. 13 827 217

591. A drop hammer weighing 40 kN is dropped freely and drives a concrete pile 150 mm into the ground. The velocity of the drop hammer at impact is 6 m/s. What is the average resistance of the soil in kN?

- a. 542.4
- b. 489.3
- c. 384.6
- d. 248.7

592. A force of 200 lbf act on a block at an angle of 28° with respect to the horizontal. The block is pushed 2 feet horizontally. What is the work done by this force?

- a. 320 J
- b. 480 J
- c. 540 J
- d. 215 J

593. A small rocket propelled test vehicle with a total mass of 100 kg starts from rest at A and moves with negligible friction along the track in the vertical plane as shown. If the propelling rocket exerts a constant thrust T of 1.5 kN from A to position B. where it is shut off, determine the distance S that the vehicle rolls up the incline before stopping. The loss of mass due to the expulsion of gases by the rocket is small and may be neglected.

- a. 170 m
- b. 165 m
- c. 160 m
- d. 175 m

594. A body that weighs W Newton fall from rest from a height 600 mm and strikes a spring whose scale is 7 N/mm. If the maximum compression of the spring is 150 mm, what is the value of W? Disregard the mass of spring.

- a. 101 N
- b. 105 N
- c. 112 N
- c. 132 N

595. A 100 N weight falls from rest from a height of 500 mm and strikes a spring which compresses by 100 mm. Compute the value of the spring constant, neglecting the mass of the spring.

- a. 10 N/mm
- b. 15 N/mm
- c. 12 N/mm
- d. 8 N/mm

596. A 200 N weight falls from rest at height “h” and strikes spring having a spring constant of 10 N/mm. the maximum compression of spring is 100 mm, after the weight the weight strikes the spring. Compute the value of h is meter.

- a. 0.12 m
- b. 0.10 m
- c. 0.15 m
- d. 0.21 m

597. A block weighing 500 N is dropped from a height of 1.2 m upon a spring whose modulus is 20 n/mm. What velocity will the block have at the instant the spring is deformed 100 mm?

- a. 6.55 m/s^2
- b. 5.43 m/s^2
- c. 4.65 m/s^2
- d. 3.45 m/s^2

598. A 50 kg object strikes the unstretched spring to a vertical wall having a spring constant of 20 kN/m. Find the maximum deflection of the spring. The velocity of the object before it strikes the spring is 40 m/s.

- a. 1 m
- b. 2 m
- c. 3 m
- d. 4 m

599. A large coil spring with a spring constant k = 120 N/m is elongated, within its elastic range by 1 m. Compute the store energy of the spring in N-m.

- a. 40
- b. 50
- c. 60
- d. 120

600. To push a 25 kg crate up a 27° inclined plane, a worker exerts a force of 120 N, parallel to the incline. As the crate slides 3.6 m, how much is the work done by the worker and by the force of gravity.

- a. 420 Joules
- b. 400 Joules
- c. 380 Joules
- d. 350 Joules

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