2005 - JAMB Physics Past Questions and Answers - page 5

41
Two liquids L1 and L2 are contained in a U - tube. The height and the density of L1 are 8 cm and 103 kgm-3 respectively. If the density of L2 is 800 kgm-3, its height measured from the same level is
A
8 cm
B
10 cm
C
16 cm
D
12 cm
correct option: b

Generally, from Hares Experiment, density is inversely proportional to height

i.e h ∝1/d; → h1d1 = h2d2

∴ 8 x 103 = h2 x 800

∴ h2 = 8 x 103
_800

= 10cm

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42
106J of heat is required to boil off completely 2kg of a certain liquid. Neglecting heat lost to the surroundings, the latent heat of vaporization of the liquid is
A
2.0 x 106J kg-1
B
5.0 x 106J kg-1
C
2.0 x 105J kg-1
D
5.0 x 105J kg-1
correct option: d

From the heat exchange involved, the latent heat of vaporization, L can be deduced from the relation:

ML = 106, where M = mass of the liquid.

∴ 2 x L = 106

=> L = 106/2 = 5.0 x 105J kg-1

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43
The figure above shows three capacitors, 2μF, 3μF and 6μF connected in series. If the p.d across the system is 12V, the p.d, across the 6μF capacitor is
A
4V
B
12V
C
2V
D
6V
correct option: c

The effective capacitance in the circuit is given by:

1/C = 1/2 + 1/3 + 1/6 = 6/6

therefore C = 1μF or

1.0 x 10-6F.

Since C = Q/V, its implies that the charges Q, flowing in the circuit is given by Q = CV

= 1.0 x 10-6 x 12

= 12.0 x 10-6 Coulomb.

∴ P.d across the 6μF,

V = Q/C = 12.0 x 10-6
6.0 x 10-6F

= 2.0 volts

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44
If the distance between two point charges its increased by a factor of four, the magnitude of the electrostatic force between them will be
A
1/4 of its former value
B
1/16 of its former value
C
1/2 of its former value
D
4 times its former value
correct option: b

For the two point charges, the magnitude of the electrostatic force between them is given by the equation:

F ∝ 1/r2, and if the distance is increased by a factor of 4, that is new distance = 4r,

then, new force F ∝ 1/(4r)2

= ∝ 1/16r2

Thus it will be 1/16 of the former value

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45
The velocity of sound in air will be doubled if it's absolute temperature is
A
Quadrupled
B
Constant
C
Halved
D
Doulbed
correct option: a

In general, the velocity of sound in air varies directly as the square root of temperature measured in kelvin.

That V ( \propto \sqrt{T} \implies V^2 \propto T. \

\text{Therefore} \frac{V^2_1}{T_1} = \frac{V^2_2}{T_2} \

\text{Thus Let } V_1 = 4m/s \

  T_1 = 10K \\

\text{Therefore } V_2 = 2V_1 = 8m/s \

\implies \frac{4^2}{10} = \frac{8^2}{T_2} \

T_2 = \frac{64 \times 10}{16} = 40K\

T_2 = 4T_1 )

Thus when the velocity of sound in air is doubled, it's absolute temperature will be quadrupled.

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46
A force of 200N acts between two objects at a certain distance apart. The value of the force when the distance is halved is
A
400N
B
200N
C
100N
D
800N
correct option: d

let the masses of the two objects be M1 and M2

and their distance apart = r

Therefore the force acting F1 = ( \frac{GM1M2}{r^2} )

for a new distance of r/2, we have a force of

F2 = ( \frac{GM2M2}{r/2} \

\text{Thus } F1 \times r^2 = GM1M1 \text{and} \

      F2 \times (r/2)^2 = GM1M1 \\

\text{Since } GM1M1 = GM1M1 \

\implies F1 \times r^2 = F2 \times (r/2)^2 \

\text{Therefore } 200 \times r^2 = F2 \times r^2/4 \

F2 = \frac{4 \times 200 \times r^2}{r^2} = 800N )

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47
If two inductors of inductances 3H and 6H are arranged in series, the total inductance is
A
9.0H
B
18.0H
C
0.5H
D
2.0H
correct option: a

l =l1 + l2 = 3 + 6 = 9H

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48
Am elastic material has a length of 36cm when a load of 40N is hung on it and a length of 45cm when a load of 60N is hung on it. The original length of the string is
A
12cm
B
20cm
C
18cm
D
15cm
correct option: c

For Hooke's law F = Ke

( \implies F/e = K \

f1/e1=f2/e2 \

\text{Let the original length} = t_0 \

\text{therefore} e1 = (36 - t_0)cm ; e2 = (46 - t_0)cm \

\text{if f1} = 40N \text{f2} = 60N \

\text{Then } \frac{40}{36 - t_0} = \frac{60}{45 - t_0} \

\implies 40(45 - t_0) = 60(36 - t_0) \

\text{therefore } 1800 - 40t_0 \

 2160 - 60t_0 \\

60t_0 - 40t_0 = 2160 - 1800 \

20t_0 = 360  \  <br />

t_0 = 18cm \)
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