JAMB UTME - Physics - 1987

A radioactive sample initially contains N atoms. After three half-lives the number of atoms that have disintegrated is

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N $\to$ $\frac{N}{2}$ $\to$ $\frac{N}{4}$ $\to$ $\frac{N}{8}$

A wave has a frequency of 2Hz and a wavelength of 30cm. The velocity of the wave is

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V = F$\lambda$

= 2 x 0.3

= 0.6ms-1

A pool of water appears to be 1.0m deep when viewed vertically from above. If the refractive index of water is 1.33, what is the actual depth of the pool?

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n = $\frac{\text{real depth}}{\text{apparent depth}}$

1.33 = $\frac{\text{real depth}}{1}$

real depth = 1.33cm

he lowest note emitted by a stretched string has a frequency of 40Hz. How many overtones are there between 40Hz and 150Hz?

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In stretched strings the overtones are in odd multiple of Fo.

F1 = 3Fo

= 3 x 40 = 120Hz

F2 = 5Fo

= 5 x 40

= 200Hz

The distance between the fixed points of a centigrade thermometer is 20cm. What is the temperature when the mercury level is 4.5cm above the lower mark?

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20cm .... 100oC

4.5cm .... $\theta$

0cm ....0oC

$\frac{4.5-0}{20-0}$ = $\frac{0-0}{100-0}$

$\theta$ = 22.5oC

As a result of air at the top of a barometer, the height of the mercury column is 73.5cm when it should be 75.0cm; the volume of the space above the mercury is 8.0cm3. Calculate the correct barometer height when the barometer reads 74.0cm and the volume of the space above the mercury is 6.0cm3.

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Using, P1P1 = P2P2

(75 - 73.5) x 8 = (X - 74) x 6

X = 76cm

In the figure above, M and N are insulated metal spheres in contact. A negatively charged ebonite rod P is I brought near M. When M and N are Separated and the rod is taken away, which of the following statements is correct

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A man walks 8km north and then 5km in a direction 60o east of north. Find the distance from his starting point

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R = $\sqrt{5^2+8^2-2\times 5\times 8\times cos{120}^o}$

R = $\sqrt{129}$

= 11.36km

A body rolls down a slope from a height of 100m. its velocity at the foot of the slope is 20ms-1. What percentage of its initial potential energy is converted into kinetic energy? [g = 10ms-1]

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P.E = mgh = 1000m joules

K.E = $\frac{1}{2}$mv2 = 200m joules

%converted = $\frac{200m}{1000m}$ x 100

= 20%

What type of reaction is represented by the following scheme? ${}_1^{2}X$ + ${}_1^{2}Y$ + ${}_2^{3}Z$ + ${}_0^{1}n$ + energy

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Calculate the amount of heat required to convert 2kg of ice at 2oC to water at 0oC. [specific heat capacity of ice = 2090Jkg-1oC-1, specific latent heat of fusion of ice = 333kJkg-1]

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Q = mL + mc$\theta$

= (2 x 333000) + (2 x 2090 x 2)

= 674 360J

Isotopes are nuclei which have

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An elevator of mass 4800kg is supported by a cable which can safely withstand a maximum tension of 60 000N. The maximum upward acceleration the elevator can have is

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a = $\frac{F}{m}$

= $\frac{60000-(4800\times 10)}{4800}$

= 2.5ms-2

If a beaker is filled with water it is observed that the surface of the water is not horizontal at the glass-water interface. This behavior is due to

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An object 3.0cm high is placed 60.0cm from a converging lens whose focal length is 20.0cm. Calculate the size of the image formed

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F = $\frac{UV}{U+V}$

20 = $\frac{60\times V}{60+V}$

V = 30cm

similarly, $\frac{U}{V}$ = $\frac{\text{height of object}}{\text{height of image}}$

$\frac{60}{30}$ = $\frac{3}{h}$

h = 1.5cm

A jet engine develops a thrust of 270Ns when the velocity of the exhaust gases relative to the engine is 300ms-1. What is the mass of the material ejected per second?

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Thrust = force x time

thrust = $\frac{m(v-u)}{t}$ x $\frac{t}{1}$

270 = m(300 - 0)

m = 0.90kg

The mechanical advantage (MA) of an inclined plane depends on

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When two parallel wires carry currents in opposite directions, the force on either wire is

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Which of the following statements is TRUE of photoelectric effect?

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The direction of the magnetic field at a point in the vicinity of a bar magnet is

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A cube of side 10cm and mass 0.5kg floats in a liquid with only $\frac{1}{5}$ of its height above the liquid surface. What is the relative density of the liquid?

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Height below liquid = 1 - $\frac{1}{5}$ = $\frac{4}{5}$

volume of cube = 103cm3

volume of liquid displaced = $\frac{4}{5}$ x 1000

= 800cm3

density of liquid displaced;

= $\frac{500}{800}$

= 0.625cm-1

The fig above represents the main sequence of energy conversion at Kainji dam. What is the efficiency of the system?

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Two capacitance of 6$\mu$F and 8$\mu$F are connected in series. What additional capacitance must be connected in series with this combination to give a total of 3$\mu$F

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3 = $\frac{6\times 8\times c}{(6\times 8)+(6\times c)+(8\times c}$

therefore, C = 24$\mu$F

Four lenses are being considered for use as a microscope objective. Which of the following focal lengths is most suitable?

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When the length I of a piece of wire under constant tension is varied, the relationship of the frequency of the vibration f$\alpha$/ is

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F = $\frac{1}{2L}\sqrt{\frac{T}{m}}$

A constant force of 40N acting on a body initially at rest gives an acceleration of 0.1ms-2 for 4s. Calculate the work done by the force

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X = ut + $\frac{1}{2}$at2

= (0 x 4) + ($\frac{1}{2}$ x 0.1 x 4 x 4)

= 0.8m

workdone = force x distance

= 40 x 0.8

= 32J

Which of the following units is equivalent to kgms-1?

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kgms-1 = $\frac{mass}{distance}$

since, F = ma = kgms-1 = N

kgms-1 = Ns

A boat at anchor is rocked by waves whose crest are 100m apart and whose velocity is 25ms-1. At what interval does the wave crest reach the boat?

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Distance between the boat and crest = 100m

time = $\frac{100}{25}$

= 4sec

22,000J of heat is required to raise the temperature of 1.5kg of paraffin from 20oC to 30oC. Calculate the specific heat capacity of paraffin.

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22,000 = 1.5 x c x (30 - 20)

c = 1466Jkg-1oC-1

Hot water is added to three times its mass of water at 10oC and the resultant temperature is 20oC. What is the initial temperature of the hot water?

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Heat loss = heat gained

mh x ch x $\theta$h = mc x cc x $\theta$c

mh x ch x ($\theta$ - 20) = mc x cc x (20 - 10)

ch = cc ; mc = 3mh

therefore, $\theta$ = 50oC

Which of the following instruments has a pure tone?

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The length of a side of a metallic cube at 20oC is 5.0cm. Given that the linear expansivity of the metal is 4.0 x 10-5k-1, find the volume of the cube at 120oC .

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Y = $\frac{V_2-V_1}{V_1\times \theta }$

3 x 4 x 10-5 = $\frac{V_2-125}{125\times (120-20)}$

V2 = 126.50cm3

A ray of light is incident at an angle of 30o on one top surface of a parallel-sided glass block of refractive index 1.5. The ray finally emerges from the lower surface. What is the angular deviation of the emergent ray?

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In which of the following are the substance arranged in descending order of their thermal conductivities?

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The velocity time graph above describes the motion of a particle between two points P and Q. What is the distance between P and Q?

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If an object is placed in front of two mirrors inclined at 90o, how many images will be formed?

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n = $\frac{360}{\theta }$ - 1

= 360 - 1

= 3 images

The fig above shows two connected bodies of masses M1 and M2 in equilibrium under gravity. The tension in the upper string is

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In the above, a voltage V is applied across the terminals P and Q. The voltage across the 1 ohm resistor is

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A galvanometer of resistance 20$\Omega$ is to be provided with a shunt that $\frac{1}{10}$ of the whole current in a circuit passes through the galvanometer. The resistance of the shunt is

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$\frac{1}{10}$I x 20 = $\frac{9}{10}$I x Rs

Rs = 2.22$\Omega$

A 50kg block is dropped from a point 10cm above as shown in the fig above. if the force constant of the spring is 4.0 x 104Nm-1, find the maximum compression of the spring [g = 10ms-2]

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Which of the following phenomena explains the fact that a house whose roof is coated with white paint will be cooler in the hot season than one coated with black paint ?

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he coefficient of static friction between a 40kg crate and concrete surface is 0.25. Find the magnitude of the minimum force needed to keep the crate stationary on the concrete base inclined at 45o to the horizontal. [G = 10ms-1]

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momentum force = R5n$\theta$ - $\mu$Rcos$\theta$

Fm = (40 x 10 x sin 45) - (40 x 10 x 0.25 x cos 45)

= 212N

When a transformer has more secondary windings than primary windings, it

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A load of 5N gives an extension of 0.56cm in a wire which obeys Hooke's law. What is the extension caused by a load of 20N?

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$\frac{F_1}{e_1}$ = $\frac{F_2}{e_2}$

$\frac{5}{0.56}$ = $\frac{20}{e_2}$

e2 = 2.24cm

Which of the following statements supports the assumption that light travels in straight lines?

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A current of 0.5A flows through a resistor when connected to a 40-V battery. How much energy is dissipated in 2 minutes?

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Electrical energy = IVT

= 0.5 x 40 x 2 x 60

= 2400J

The vacuum in a thermos flask helps to reduce heat transfer by?

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