JAMB UTME - Physics - 1985

In a gas experiment, the pressure of the gas is plotted against the reciprocal of the volume of the gas at a constant temperature. the unit of the slope of the resulting curve is

Détails de la réponse

slope = pressure $÷$ $\frac{1}{volume}$

= $\frac{N}{m^3}$ x $\frac{m^3}{1}$

= Nm = work

A metal block of mass 5kg lies on a rough horizontal platform. If a horizontal force of 8N applied to the block through its center of mass just slides the block on the platform, then the coefficient of limiting friction between the block and platform is

Détails de la réponse

F = $\mu$R

= $\mu$mg

8 = $\mu$ x 5 x 10

$\mu$ = 0.16

Two divers G and H are at depths 20m and 40m respectively below the water surface in a lake. The pressure on G is P1 while the pressure on H is P2. If the atmospheric pressure is equivalent to 10m of water, then the value of $\frac{p_2}{p_1}$ is

Détails de la réponse

pressure at H = 40m ; pressure at G, p1 = 20m

$\frac{p_1}{p_1}$ = $\frac{40}{20}$

= 2

Two rays of light from a point below the surface of water are equally inclined to each other at 60o in water. What is the angle between the rays when they emerge into air? (Take the refractive index of water to be $\frac{4}{3}$)

Détails de la réponse

$\frac{4}{3}$ = $\frac{sin{r}_1}{sin30}$ and $\frac{4}{3}$ = $\frac{sin{r}_2}{sin30}$

r1 = 41.8o and r2 = 41.8o

angle between them = r1 + r2

= 83.6o

In the Fig above, MN is a light uniform meter rule pivoted at O, the 80cm mark. A load of mass 3.00kg is suspended on the meter rule at L, the 10cm mark. If the rule is kept in equilibrium by a string RP, fixed at P and attached to the rule at R, the 20cm mark, then the Tension T on the string is

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A charge of one coulomb liberates 0.0033g of copper in an electrolytic process. How long will it take a current of 2A to librate 1.98g of copper in such a process?

Détails de la réponse

0.0033g = 1 coulomb

1.98gs = 1.98 x 1

= 600 cou.

Q = It

600 = 2 x t

t = 300sec = 5 mins

In the Fig above, Current I passes through the combination, if the power dissipated in the 5 ohm resistor is 40W, then the power dissipated in the 10 ohm resistor is

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A block of mass 2.04kg resting on a smooth horizontal plane is acted upon simultaneously by two-forces, 10N due North and 10N due East. The magnitude of the acceleration produced by the force on the block is

Détails de la réponse

R = $\sqrt{{10}^2+{10}^2}$

R = 14.14N

R = F = ma

14.14 = 2 x a

a = 7.07ms-1

Which of the following types of motion are oscillatory? i.a diving board when used by a diver. ii. the motion of the balance wheel of a wrist watch. iii. the motion of the turn-table of a record player. iv. the motion of the center of a ten kobo piece as it rolls down an inclined plane. v. the motion of the needle of a D.C. ammeter into which a low A.C. current is passed

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What is the number of neutrons in the Uranium isotope ${}_{92}^{238}X$?

Détails de la réponse

No of neutrons = 238-92

=146

Which of the following methods CANNOT be used to produce a steel magnet? The

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If a car starts from rest and moves with a uniform acceleration of 10ms-2 for ten seconds, the distance it covers in the last one second of its motion is

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Distance in 105, using, x = ut + $\frac{1}{2}$at2

x = (0 x 10) + ($\frac{1}{2}$ x 10 x 10 x 10) = 500m

distance in 9s; x - (0 x 9) + ($\frac{1}{2}$ x 10 x 9 x 9) = 405m

distance in last is = difference

= 500 - 405

= 95m

If the fundamental frequency of a closed pipe organ on a day when the speed of sound is 340ms-1 is 170Hz, then the length of the pipe is

Détails de la réponse

$\lambda$ = $\frac{v}{f}$

= $\frac{340}{170}$

= 2m ; for closed pipe

L = $\frac{1}{4}$$\lambda$

= $\frac{1}{4}$ x $\frac{2}{1}$

= 0.5m

= 50cm

A quantity of gas occupies a certain volume when the temperature is -73oC and the pressure is 1.5 atmospheres. If the pressure is increased to 4.5 atmospheres and the volume is halved at the same time, what will be the new temperature of the gas?

Détails de la réponse

$\frac{P_1{V}_1}{T_1}$ = $\frac{P_2{V}_2}{T_2}$

V1 = 2V2

$\frac{1.5\times 2V_2}{-73+273}$ = $\frac{4.5\times V_2}{T_2}$

T2 = 300K = 27oC

A 45o triangular glass prism can be used as a reflector of light because

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A cell gives a current of 0.15A through a resistance of 8$\Omega$ and 0.3A. When the resistance is changed to 3$\Omega$ the internal resistance of the cell is

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Which of the following is NOT a force?

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A 0.05kg bullet travelling at 500ms-1 horizontally strikes a thick vertical wall. It stops after penetrating through the wall horizontal distance of 0.25m. What is the magnitude of the average force the wall exerts on the bullet?

Détails de la réponse

F = ma

= m$\frac{(v^2-u^2)}{2s}$

F = 0.05$\frac{(0-(500{)}^2)}{2\times 0.25}$

F = 25 000N

Which of the following features is NOT a characteristic of natural radioactivity?

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Which of the following statements about electrolysis is NOT correct?

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An object is placed 15cm in front of a concave mirror of radius 40cm. The image formed

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u = f

A narrow beam of white light can be split up into different colours by a glass prism. The correct explanation is that

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Which of the following statements is NOT correct?

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Normal atmospheric pressure at sea-level is 105Nm-2 and the acceleration due to gravity is approximately 10ms-1. If the atmosphere has a uniform density of 1kgm-3, its height is

Détails de la réponse

pressure = h x g x e

105 = 10 x h x 1

h = 104

On which of the following does the operation of a moving coil ammeter depend? i. Electromagnetic induction ii. Force on a carrying-current conductor iii. Magnetic effect of an electric current

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Which of the following statements is NOT correct?

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A good calorimeter should be of

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A force of 100N stretches an elastic string to a total length of 20cm. If an additional force of 100N stretches the string 5cm further, Find the natural length of the string

Détails de la réponse

Using, f1 = f2

e1 = 20 - L ; e2 = 5cm

$\frac{f_1}{e_1}$ = $\frac{f_2}{e_2}$

$\frac{100}{20-L}$ = $\frac{100}{5}$

hence, L = 15cm

A simple pendulum with a period of 2.0s has its length doubled. Its new period is

Détails de la réponse

Using $\frac{T_1}{T_2}$ = $\sqrt{\frac{L_1}{L_2}}$

$\frac{2}{T_2}$ = $\sqrt{\frac{L_1}{2L_1}}$

T2 = 2.83sec

In order to find the depth of the sea, a ship sends out a sound wave and receives an echo after one second. If the velocity of sound in water is 1500ms-1, what is the depth of the sea?

Détails de la réponse

Echo time = 1 $÷$ 2 = 0.5sec

depth = velocity x time

= 1500 x 0.5

= 750m = 0.75km

Which of the following statements are NOT correct?

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Water shows anomalous behaviour

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Which of the following will convert a milliammeter to a voltmeter?

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An electric kettle, connected to a 240V mains, produces 6.0 x 105J of heat energy to boil a quantity of water in 5 minutes. Find the resistance of the kettle.

Détails de la réponse

Heat energy = Electrical energy

6 x 105 = $\frac{V^2}{R}$t

R = $\frac{240\times 240\times 5\times 60}{6\times 105}$

= 28.8$\Omega$

Which of the following phenomena CANNOT be explained by the molecular theory of matter?

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The areas of the effort and load pistons of a hydraulic press are 0.5m2 and 5m2 respectively. If a force F1 of 100N is applied on the effort piston, the force F2 on the load is

Détails de la réponse

$\frac{load}{area}$ = $\frac{effort}{area}$

$\frac{load}{5}$ = $\frac{100}{0.5}$

load = 1000N

Two liquids, P at a temperature of 20oC and Q at a temperature of 80oC have specific heat capacities of 1.0Jkg-1oC-1 and 1.5J kg-1oC-1respectively. if equal masses of P and Q are mixed in a lagged calorimeter, then the equilibrium temperature is

Détails de la réponse

Heat lost = heat gained

m x (80 - $\theta$) x 1.5 = m x ($\theta$ - 20) x 1

$\theta$ = 56oC

Which of the following is NOT a fundamental S.I unit?

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When a sound wave passes from air into water its

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Two masses 40g and 60g respectively, are attached firmly to the ends of the light meter rule. The center of gravity of the system is

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If the distance between two stationary charged particle is doubled, the magnitude of the electro-static force between them will be

Détails de la réponse

F $\alpha$ $\frac{1}{d^2}$

F x d2 = constant

F1 x (d1)2 = F2 x (d2)2

d2 = 2d1

F1 x (d1)2 = F2 x (2d1)2

F2 = $\frac{1}{4}$F1

Which of the following statements are true about the spring balance and the chemical balance? i. both are used to measure the mass of an object. ii. either of them may be used to measure the weight of an object. iii. the spring balance works on the principle of Hooke's law while the chemical balance works on the principle of moments. iv. a change in gravity does the readings of a spring balance but not that of a chemical balance.

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Two thermo flasks of volume Vx and Vy are filled with liquid water at an initial temperature of 0oC. After sometime the temperature were found to be 9x, 9y, respectively. Given that $\frac{Vx}{Vy}$ = 2 and $\frac{\theta x}{\theta y}$ = $\frac{1}{2}$ the ratio of the heat flow into the flask is

Détails de la réponse

Heat = mc$\theta$

Hx = Dx x Vx x Cx x $\theta$x

Hy = Dy x Vy x Cy x $\theta$y

$\frac{H_x}{H_y}$ = $\frac{D_x\times V_x\times C_x\times {\theta }_x}{D_x\times V_x\times C_x\times {\theta }_x}$

= 2 x $\frac{1}{2}$

= 1

A uniform cylindrical block of wood floats in water with one-third of its height above the water level, in a liquid of relative density 0.8, what fraction of its height will be above the liquid level?

Détails de la réponse

Height inside H2O = $\frac{2}{3}$

R.d = $\frac{\text{height inside}{H}_{2}O}{\text{height inside liquid}}$

0.8 = $\frac{\frac{2}{3}}{X}$

A thin aluminum plate has a surface area of 1500m at 20oC. What will be its surface area when it is cooled to -20oC? (Take the linear expansivity of aluminum to be 2.5 x 10-5k-1).

Détails de la réponse

$\beta$ = A2 - A1

2 X 10-5 x 2.5 = $\frac{A_2\times 1.5}{1.5\times (-20-20)}$

A2 = 1.498m2

A wire P has half the diameter and half the length of a wire Q of similar material. The ratio of the resistance of P to that of Q is

Détails de la réponse

Resistance $\alpha$ $\frac{length}{area}$

$\frac{R_Q}{R_P}$ = $\frac{L_Q{A}_P}{L_P{A}_Q}$

LQ = 2LP

DQ = 2DP

AP = $\pi$$\frac{(2D_P{)}^2}{2}$

= $\pi$DP

AQ = $\pi$$\frac{(D_P{)}^2}{2}$

= $\frac{1}{4}$$\pi$DP

therefore, $\frac{R_Q}{R_P}$ = $\frac{2L_P\times \pi D_P}{L_P\times \frac{1}{4}\pi D_P}$

= 2 : 1

The graph in the fig above describes the motion of a particle. the acceleration of the particle during the motion is

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A transformer has a primary coil with 500 turns and a secondary coil with 2500 turns. When the voltage input to the primary coil is 120V, the output is

Détails de la réponse

For transformers, $\frac{V_p}{V_s}$ = $\frac{N_p}{N_s}$ = $\frac{I_p}{I_s}$

$\frac{500}{2500}$ = $\frac{120}{V_s}$

Vs = 600v

A convex mirror is used as a driving mirror because i. its image is erect. ii. it has a large field of view. iii. it has a long focal length. Identify the CORRECT statement(s)

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A metal cube of volume 103mm3 is lowered into a measuring cylinder containing water. If the internal cross-sectional area of the cylinder is 1.5 x 102mm2, by how much does the water level rise in the cylinder?

Détails de la réponse

Height = $\frac{volume}{area}$

= Height = $\frac{{10}^3}{1.5\times {10}^2}$

= 6.67mm