How to solve questions on simple machine and light waves for UTME

How to solve questions on simple machine and light waves for UTME

Question 1

A ray of light strikes a plane mirror at an angle of incidence of 35o. If the mirror is rotated through 10o, through what angle is the reflected ray rotated?{utme 2001}
A. 45o          B. 20o              C. 70o                     D. 25o

The reflected ray will rotate through the angle = 2* angle through which the mirror rotate = 2*10 =20

B is the correct option

Question 2

A wheel and axle is used to raise a load of 500 N by the application of an effort of 250N. If the radii of the wheel and
the axle are 0.4cm and o.1cm respectively, the efficiency of the machine is {2002}
A. 20%                     B. 40%                  C. 50%                         D. 60%

Solution

velocity ratio = radius of wheel / radius of axle = 0.4 / 0.1 = 4

mechanical advantage = load / effort = 500 / 250 = 2

efficiency = m.a /v.r *100% = 2/4 *100% = 50%

C is the correct option

Question 3

A concave mirror of radius of curvature 40cm forms a real image twice as large as the object. The object distance is

{utme 2002}
A. 10cm                      B. 30cm                 C. 40cm                            D. 60cm.

Solution

radius = 2f

f = 40/2 = 20cm

v = image, u = object

v = 2*u = 2u

1/f = 1/u + 1/v

1/20 = 1/u + 1/2u

1/20 = 3/2u

cross mutiply

2u = 60

u = 60/2 = 30cm

B is the correct answer

Question 4

To produce an enlarged and erect image with a concave mirror, the object must be positioned{2002}
A. at the principal focus.       B. beyond the centre of curvature        C. between the principal focus and
the centre of curvature.         D. between the principal focus and the pole.

D is the correct option

Question 5

By what factor will the size of an object placed 10cm from a convex lens be increased if the image is seen on a screen placed 25cm from the lens?{utme 2003}
A. 15.0                    B. 2.5                      C. 1.5                    D. 0.4

Solution

magnification = image distance / object distance = 25 / 10 = 2.5

B is the correct option

Question 6

If an object is placed between two parallel plane mirrors with their reflecting surfaces facing each other, how many images of the object will be formed?
A. Infinite             B. Eight            C. Four                 D. Two.

Solution

N =( 360/θ) – 1

Where the angle of inclination and N is the number of images formed

angle between two parallel mirrors is 0

N = 360/0 -1 = infinity

A is the correct option

Question 7

At what position will an object be placed in front of a concave mirror in order in order to obtain an image at
infinity?{utme 2003}
A. At the pole of the mirror.      B. At the principal focus.               C. At the centre of curvature             D. Between the principal focus and the centre of curvature.

Solution

B is the correct option

Question 8

A machine whose efficiency is 60% has a velocity ratio of 5. If a force of 500N is applied to lift a load P, what is the
magnitude of P?{utme 2004}
A. 750N                 B. 4166N                  C. 500N                       D. 1500N

Solution

efficiency = m.a /v.r *100%

60/100 = m.a/5

cross multiply

m.a = 300/100 = 3

m.a = load / effort

3 = p / 500

p = 1500N

D is the correct answer
short note on optics