MCQ in Engineering Mechanics Part 8 | ECE Board Exam

This is the Multiple Choice Questions Part 8 of the Series in Engineering Mechanics as one of the General Engineering and Applied Sciences (GEAS) topics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize yourself with each and every question compiled here taken from various sources including past Board Questions in General Engineering and Applied Sciences (GEAS) field, GEAS Books, Journals, and other GEAS References.

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⇐ MCQ in Engineering Mechanics Part 7 | ECE Board Exam

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351. A simply supported beam is 5 meters in length. It carries a uniformly distributed load including its own weight of 300 N/m and a concentrated load of 100 N, 2 meters from the left end. Find the reactions if reaction A is at the left end and reaction B at the right end.

A. Ra = 810 N & Rb = 700 N

B. Ra = 700 N & Rb = 800 N

C. Ra = 810 N & Rb = 780 N

D. Ra = 700 N & Rb =8 10 N

352. A beam of span ‘x’ meters with uniform loading of ‘w’ kilograms per meter is supported at one end (A) and a distance of 2 m from the other end (B). Find the reaction at support A.

A. (wx^2)/ [2(x-2)] kg

B. [wx(x-4)]/[2(x-2)] kg

C. [wx(x-2)]/[2(x-2)] kg

D. wx/[2(x-2)] kg

353. When one boy is sitting 1.2 m from the center of a see-saw, another boy must to sit on the other side 1.5 m from the center to maintain an even balance. However, when the first boy carries an additional weight of 14 kg and sit 1.8 m from the center, the second boy must move to 3 m from the center to balance. Neglecting the weight of the see-saw, find the weight of the heavier boy.

A. 30 kg

B. 42 kg

C. 34 kg

D. 45 kg

354. A 40 kg block is resting on an inclined plane making an angle of 20° from the horizontal. If the coefficient of friction is 0.60, determine the force parallel to the incline that must be applied to cause impending motion down the plane.

A. 82

B. 77

C. 87

D. 72

355. A 250 lb. block is initially at rest on a flat surface that is inclined at 30°. If the coefficient of kinetic friction is 0.30 and the coefficient of static friction is 0.40, find the force required to start the block moving up the plane.

A. 190 lb

B. 212 lb

C. 125 lb

D. 75 lb

356. A 600 N block rests in a surface inclined at 30°. Determine the horizontal force P required to prevent the block from sliding down. Angle of friction between the block and the inclined plane is 15°.

A. 160.75 N

B. 198.55 N

C. 164.60 N

D. 190.45 N

357. Assume the three force vectors intersect at a single point.

F1 = 4i + 2j + 5k

F2 = –2i + 7j – 3k

F3 = 2i – j + 6k

What is the magnitude of the resultant force vector, R?

A. 14

B. 12

C. 13

D. 15

358. Given the 3-dimensional vectors:

A = i(xy) + j(2yz) + k(3zx)

B = i(yz) + j(2zx) + k(xy)

Determine the magnitude of the vector sum |A + B| at coordinates (3,2,1).

A. 32.92

B. 29.92

C. 27.20

D. 24.73

359. At what angle does the force F = 6.23i – 2.38j +4.92 kN makes with the x-axis?

A. 39.2 deg

B. 40.2 deg

C. 41.3 deg

D. 42.2 deg

360. Assume the three force vectors intersect at a single point.

F1 = i + 3j + 4k

F2 = 2i + 7j – k

F3 = -i + 4j + 2k

What is the magnitude of the resultant force vector, R?

A. 15

B. 13.23

C. 14.73

D. 16.16

361. A certain cable is suspended between two supports at the same elevation and 500 ft apart, the load is 500 lbs. per horizontal foot including the weight of the cable. The sag of the cable is 30 feet. Calculate the total length of the cable.

A. 503.76 ft.

B. 502.76 ft

C. 504.76 ft

D. 501.76 ft

362. A cable supported at two points of same level has a unit weight, ω of 0.02 kg per meter of horizontal distance. The allowed sag is 0.02 m and a maximum tension at the lowest point of 1200 kg and a factor of safety of 2. Calculate the allowable spacing of the poles assuming a parabolic cable.

A. 64.02 m

B. 66.37 m

C. 67.76 m

D. 69.28 m

363. A cable carrier a horizontal load of 20 kg/m. Neglecting its own weight, find the maximum tension on the cable if the distance between the supports is 100 m and the sag is 5 m.

A. 5099 kg

B. 5059 kg

C. 5199 kg

D. 5215 kg

364. Determine the sag of a flexible wire cable weighing 60 N/m over two frictionless pulleys 100m apart and carrying one 10 kN weight at each end. Assume the weight of the cable to be uniformly distributed horizontally. The cable extends 5 m beyond each pulley to the point they are attached to the weights.

A. 7.2 m

B. 7.4 m

C. 7.6 m

D. 7.8 m

365. A copper cable is suspended between two supports on the same level, spaced 600 m apart. The cable hangs under the influence of its own weight only. Under these conditions, it is desired to calculate the maximum sag (at the center of the span) when the maximum stress in the material is 1000 kg/cm^2. The cross section of the cable is 1.77 sq. cm. weight of the cable = 1.5 kg/m. Use parabolic equation.

A. 42.26 m

B. 43.26 m

C. 44.26 m

D. 45.26 m

366. A cable weighing 0.4 kg/m and 800m long is to be suspended with a sag of 80 m. Determine the maximum tension.

A. 414 kg

B. 420 kg

C. 416 kg

D. 400 kg

367. A cable weighing 60 N/m is suspended between two supports on the same level at 300 m apart. The sag is 60 m. Compute the distance of the lowest point of the cable from the ground level.

A. 205.5 m

B. 196.8 m

C. 200.5 m

D. 188.2 m

368. Find the location of the centroid of the composite area consisting of a 10-inch square surmounted by a semi-circle. The centroid of a semicircle is located 4r/3π above the base (diameter) of the semi circle of radius r.

A. 6.0 inches from the bottom

B. 6.2 inches from the bottom

C. 6.4 inches from the bottom

D. 7.0 inches from the bottom

369. Electrical loads are arranged on horizontal x,y axes as follows:

Load	x-coordinate	y- coordinate	Kilowatt-load
1	0	2	100
2	1	1	180
3	1	3	200
4	2	0	120
5	2	4	150
6	3	1	200
7	3	3	180
8	4	2	100

A. x = 2.000, y = 2.049

B. x = 2.163, y = 2.195

C. x = 1.854, y = 2.211

D. x = 2.146, y = 1.902

370. A rectangle has a base of 3 cm and a height of 6 cm. What is its second moment of area (in cm^4) about an axis through the center of gravity and parallel to the base?

A. 64

B. 34

C. 44

D. 54

371. A circle has a diameter of 20 cm. Determine the moment of inertia of the circular area relative to the axis perpendicular to the area through the center of the circle in cm^4.

A. 14,280

B. 15,708

C. 17,279

D. 19,007

372. The moment of inertia of a section 2” wide x 2’ 0” high about an axes 1’0” above the bottom edge of the section is:

A. 1834 in^4

B. 384 in^4

C. 9214 in^4

D. 2304 in^4

373. An isosceles triangle has a 10cm base and a 10 cm altitude. Determine the moment of inertia of the triangular area relative to a line parallel to the base and through the upper vertex in cm^4.

A. 2750

B. 3025

C. 2500

D. 2273

374. What is the moment of inertia of a cylinder of radius 5 m and mass of 5 kg?

A. 120 kg-m^2

B. 80 kg-m^2

C. 62.5 kg-m^2

D. 72.5 kg-m^2

375. What is the inertia of a bowling ball (mass = 0.5 kg) of radius 15 cm rotating at an angular speed of 10 rpm for 6 seconds?

A. 0.001 kg-m^2

B. 0.002 kg-m^2

C. 0.005 kg-m^2

D. 0.0045 kg-m^2

376. What is the acceleration of the body that increases in velocity from 20 m/s to 40 m/s in 3 seconds?

A. 5.00 m/s^2

B. 6.67 m/s^2

C. 7.00 m/s^2

D. 8.00 m/s^2

377. How far does an automobile move while its speed increases uniformly from 15 kph to 45kph in 20 seconds?

A. 185 m

B. 167 m

C. 200 m

D. 172 m

378. A train passing point A at a speed of 72 kph accelerates at 0.75 m/s^2 for one minute along a straight path then decelerates at 1.0 m/s^2. How far in km from point A will it be 2 minutes after passing point A?

A. 3.60 km

B. 4.65 km

C. 6.49 km

D. 7.30 km

379. From a speed of 75 kph a car decelerates at the rate of 500 m/min^2 along a straight path. How far in meters will it travel in 45 seconds?

A. 790.293 m

B. 791.357 m

C. 793.238 m

D. 796.875 m

380. A train starting at initial velocity of 30 kph travels a distance of 21 km in 18 minutes. Determine the acceleration of the train at this instant.

A. 0.0043 m/s^2

B. 0.0206 m/s^2

C. 0.0865 m/s^2

D. 0.3820 m/s^2

381. An automobile moving at a constant velocity of a 15 m/sec passes a gasoline station. Two seconds later, another automobile leaves the gasoline station and accelerates at a constant rate of 2 m/sec^2. How soon will the second automobile overtake the first?

A. 15.3 sec

B. 16.8 sec

C. 13.5 sec

D. 18.6 sec

382. If a particle position is given by the expression x(t) = 3.4t^3 – 5.4t meters, what is the acceleration of the particle after t=5 seconds?

A. 1.02 m/s^2

B. 102 m/s^2

C. 3.4 m/s^2

D. 18.1 m/s^2

383. The distance a body travels is a function of time and is given by x(t) = 18t + 9t^2. Find its velocity at t=2.

A. 36

B. 54

C. 24

D. 20

384. Determine the velocity of progress with the given equation: D = 20t + 5/(t+1) when t = 4 seconds.

A. 18.6 m/s

B. 19.8 m/s

C. 21.2 m/s

D. 22.4 m/s

385. A ball is dropped from a building 100 m high. If the mass of the ball is 10 gm after what time will the ball strike the earth?

A. 4.52 s

B. 4.42 s

C. 5.61 s

D. 2.45 s

386. A ball is dropped from the roof of a building 40 meters tall will hit the ground with the velocity of;

A. 50 m/sec

B. 28 m/sec

C. 19.8 m/sec

D. 30 m/sec

387. Using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 meters per second, followed by another shot after 5 seconds. Find the initial velocity of the second ball in order to meet the first ball 150 meters from the ground.

A. 65.3 m/sec

B. 45.1 m/sec

C. 56.2 m/sec

D. 61.3 m/sec

388. A ball is thrown vertically upward from the ground and a student gazing out of the window sees it moving upward pass him at 5 m/sec. The window is 10 m above the ground. How high does the ball go above the ground?

A. 15.25 m

B. 14.87 m

C. 9.97 m

D. 11.30 m

389. A ball is dropped from a height of 60 meters above the ground. How long does it take to hit the ground?

A. 2.1 sec

B. 3.5 sec

C. 5.5 sec

D. 1.3 sec

390. A baseball is thrown from a horizontal plane following a parabolic path with an initial velocity of 100 m/s at an angle of 30° above the horizontal. How far from the throwing point will the ball attain its original level?

A. 890 m

B. 883 m

C. 880 m

D. 875 m

391. A plane dropped a bomb at an elevation of 1000 meters from the ground intended to hit the target at an elevation of 200 meters from the ground. If the plane was flying at a velocity of 300 km/hr, at what distance from the target must the bomb be dropped to hit the target. Wind velocity and atmospheric pressure to be disregarded.

A. 1024.2 m

B. 1055.6 m

C. 1075.5 m

D. 1064.2 m

392. The muzzle velocity of a projectile is 1500 fps and the distance of the target is 10 miles. The angle of elevation of the gun must be:

A. 21° 59’

B. 22° 41’

C. 24° 43’

D. 25° 18’

393. A shot is fired at an angle of 45 degrees with the horizontal and a velocity of 300 fps. Calculate, to the nearest value, the range of the projectile.

A. 932 yards

B. 1200 yards

C. 3500 yards

D. 4000 yards

394. A projectile leaves a velocity of 50 m/s at an angle of 30 degrees with the horizontal. Find the maximum height that it could reach.

A. 31.86 m

B. 31.28 m

C. 30.62 m

D. 30.12 m

395. A shot is fired with an angle of 45° with the horizontal with a velocity of 300 ft/s. Find the maximum height and range that the projectile can cover, respectively.

A. 800 ft, 1600 ft

B. 923 ft, 3500 ft

C. 700 ft, 2800 ft

D. 1800 ft, 3000 ft

396. A ball is thrown from a tower 30 m high above the ground with a velocity of 300 m/s directed at 20° from the horizontal. How long will the ball hit the ground?

A. 21.2 s

B. 22.2 s

C. 23.2 s

D. 24.2 s

397. In the last two second of NBA finals featuring Chicago Bulls VS Utah Jazz, with the latter ahead by 2 points with the former 94-92 count. Bulls Michael Jordan decides to shoot from a certain point on the rainbow territory which counts 3 point if converted. During the play, if Jordan releases the ball at 7 m from the basket and 2.15 m above the ground and an inclination of 40° with the horizontal and assuming no block was made by the opponents, at what velocity will the ball be given to cast the winning basket? The basket is 10 feet from the ground.

A. 8.57 m/s

B. 8.86 m/s

C. 9.03 m/s

D. 9.27 m/s

398. A projectile is fired with a muzzle velocity of 300 m/s from a gun aimed upward at an angle of 20° with the horizontal, from the top of a building 30 m high above a level ground. With what velocity will it hit the ground in m/s?

A. 298 m/s

B. 299 m/s

C. 300 m/s

D. 301 m/s

399. A stone is thrown upward at an angle of 30° with the horizontal. It lands 60 m measured horizontally and 2 m below measured vertically from its point of release. Determine the initial velocity of the stone in m/s.

A. 22.35 m/s

B. 23.35 m/s

C. 24.35 m/s

D. 25.35 m/s

400. A wooden block having a weight of 50 N is placed at a distance of 1.5 m from the center of a circular platform rotating at a speed of 2 radians per second. Determine the minimum coefficient of friction of the block so that it will not slide. Radius of the circular platform is 3 m.

A. 0.55

B. 0.58

C. 0.61

D. 0.65

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