All the questions below are UTME past questions

Questions 1 – 5 are from 2013 UTME

Question 1

The resultant of two forces is 50N. If the forces are perpendicular to each other and one of them makes an angle of 300 with the resultant, find its magnitude

A. 25.0N B. 100.0N C. 57.7N D. 43.3N

Solution

since the two forces are perpendicular, it can be represented using a right-angle triangle. Also one of the make an angle 30 degree with the resultant.

Using SOHCAHTOA

the resultant is the hypothenus

cos θ = adj / hyp

cos 30 = x / 50

0.866 * 50 = x

x = 43.3 N

D is the correct option

Question 2

A simple pendulum of length 0.4m has a period 2s. What is the period of a similar pendulum of length 0.8m at the same place?

Solution

cross multiply

D is the correct option

Question 3

An object is moving with a velocity of 5ms-1. At what height must a similar body be situated to have a potential energy equal in value with the kinetic energy of the moving body?

A. 1.0m B. 25.0m C. 20.0m D. 1.3m

[g ≈ 10ms-2]

Solution

K.E = Mgh

1/2 mv^2 = mgh

1/2 * m * 5^2 = m * 10* h

25 / 2 =10h

h = 25 / 20

h = 1.25 m, approximately = 1.3 m

D is the correct option

Question 4

If a sonometer has a fundamental frequency of 450Hz, what is the frequency of the fifth overtone?

A. 75Hz B. 2700Hz C. 456Hz D. 444Hz

Solution for a sonometer box

first overtone = 2f0

second overtone = 3f0

third overtone = 4fo

fourth overtone = 5f0

fifth overtone = 6f0

therefore,

fifth overtone = 6 * 450 = 2700 Hz

B is the correct option

Question 5

An electric device is rated 2000W, 250V. Calculate the maximum current it can take.

A. 6A B. 9A C. 8A D. 7A

solution

p = Iv

2000 = 250I

I = 2000 / 250

I = 8 A

C is the correct option

Question 6-8 are from 2012 UTME

QUESTION 6

Calculate the total distance covered by a train before coming to rest if its initial speed is 30ms-1 with a constant

retardation of 0.1ms-2.

A. 5500m B. 4500m C. 4200m D. 3000m

Solution

v2 = u2 + 2as

since the car is decelerating, the acceleration = – 0.1 ms-2

0 = 30^2 – 2 * -0.1 * s

0 = 900 – 0.2s

900 = 0.2 s

s = 900 / 0.2

s = 4500 m

B is the correct option

Question 7

An object moves in a circular path of radius 0.5m with a speed of 1ms-1. What is its angular velocity?

A. 8 rads-1 B. 4 rads-1 C. 2 rads-1 D. 1 rads-1

Solution

1 = ω * 0.5

ω = 1 / 0.5

ω = 2 rads-1

C is the correct option

Question 8

An object of mass 20kg slides down an inclined plane at an angle of 30o to the horizontal. The coefficient of static friction is

A. 0.2 B. 0.3 C. 0.5 D. 0.6

[g = 10ms-2]

Solution

mgsinθ – µR = 0

µ = mgsinθ / R

R = mg

µ = mgsinθ / mg

µ = sinθ

µ = sin 30 = 0.5

C is the correct option

Question 9

The equation of a wave travelling in a horizontal direction is expressed as y=15 sin (60t-πx) what is its

wavelength?

A. 60m B. 15m C. 5m D. 2m

Solution

y = A sin (ωt – ∅)

∅ = 2π /⋋

π = 2π / ⋋

⋋ = 2π / π

⋋ = 2 m

Question 10

Three similar cells each of e.m.f 2V and internal resistance 2Ω are connected in parallel, the total e.m.f and total internal resistance are respectively { UTME 2011}

A. 6 V, 0.7Ω B. 6 V, 6.0Ω C. 2 V, 0.7Ω D. 2 V, 6.0Ω

Solution

Since the cells are arranged in parallel

the e.m.f will be 2v

1/r = 1/r1 + 1/r2 + 1/r3

1/r = 1/2 + 1/2 + 1/2

1/r = 3/2

r = 2/3

r = 0.7Ω

C is the correct option