Physics 2008 Jamb Examination
Physics 2008 Jamb Examination
Question 41
If a body of mass 5 kg is thrown vertically upwards with velocity $u$, at what height will the potential energy equal the kinetic energy?
Total mechanical energy per unit mass is $\dfrac{1}{2}u^2$. If potential energy equals kinetic energy, each must be half the total. So each equals $\dfrac{1}{4}u^2$. Thus
$$gh=\dfrac{1}{4}u^2\quad\Rightarrow\quad h=\dfrac{u^2}{4g}.$$
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Question 42
Counting of currency notes with moist fingers is based on the principle of?
Moist fingertips cause notes to stick because of adhesive forces between the moist skin and the paper surface. This is adhesion.
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Question 43
A motorcycle of mass 100 kg moves round in a circle of radius 10 m with a velocity of 5 mĀ·sā»Ā¹. Find the coefficient of friction between the road and the tyres.
Centripetal force required: $F_c=\dfrac{mv^2}{r}=\dfrac{100\times5^2}{10}=\dfrac{2500}{10}=250\ \text{N}$.
Maximum friction available is $\mu mg$. So $$\mu=\dfrac{F_c}{mg}=\dfrac{250}{100\times9.8}\approx\dfrac{250}{980}\approx0.255\approx0.25.$$
Maximum friction available is $\mu mg$. So $$\mu=\dfrac{F_c}{mg}=\dfrac{250}{100\times9.8}\approx\dfrac{250}{980}\approx0.255\approx0.25.$$
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Question 44
A spring of force constant $500\ \text{NĀ·m}^{-1}$ is compressed such that its length shortens by $5\ \text{cm}$. The energy stored in the spring is?
Energy stored in a spring: $E=\dfrac{1}{2}kx^2$. With $k=500\ \text{NĀ·m}^{-1}$ and $x=0.05\ \text{m}$,
$$E=\tfrac{1}{2}\times500\times(0.05)^2=250\times0.0025=0.625\ \text{J}.$$
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Question 45
In the hare's apparatus, water rises to a height of $26.5\ \text{cm}$ in one limb. If a liquid rises to a height of $20.4\ \text{cm}$ in the other limb, what is the relative density of the liquid?
For equilibrium in connected limbs, $\rho_{liquid}\times h_{liquid}=\rho_{water}\times h_{water}$. With $\rho_{water}=1$,
$$\rho_{liquid}=\dfrac{h_{water}}{h_{liquid}}=\dfrac{26.5}{20.4}\approx1.299\approx1.3.$$
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Question 46
I. Force (N)
II. Torque (NĀ·m)
III. Current (A)
IV. Power (W)
Which of the above are the correct S.I. units of the quantities indicated?
II. Torque (NĀ·m)
III. Current (A)
IV. Power (W)
Which of the above are the correct S.I. units of the quantities indicated?
SI units: Force ā newton (N), Torque (moment) ā newton-metre (NĀ·m), Current ā ampere (A), Power ā watt (W). All four entries (I, II, III, IV) correspond to correct SI units. (The provided option set does not include all four; follow the supplied answer key if required.)
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Question 47
Which of the following is NOT a vector quantity?
Altitude (height above sea level) is a scalar (magnitude only). Acceleration, displacement and weight are vector quantities (they have direction and magnitude).
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Question 48
If a wheel 1.2 m in diameter rotates at one revolution per second, calculate the linear velocity of a point on its rim.
Diameter = 1.2 m ā radius $r=0.6$ m. Angular speed for 1 rev/s: $\omega=2\pi\ \text{radĀ·s}^{-1}$. Linear speed $v=\omega r=2\pi\times0.6=1.2\pi\approx3.7699\ \text{mĀ·s}^{-1}\approx3.77\ \text{mĀ·s}^{-1}$.
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Question 49
I. All the three forces must be concurrent.
II. The upward force is equal to the downward force.
III. The algebraic sum of the moments about any point must be zero.
Which of the above conditions must hold for a body acted upon by a system of three coplanar forces in equilibrium?
II. The upward force is equal to the downward force.
III. The algebraic sum of the moments about any point must be zero.
Which of the above conditions must hold for a body acted upon by a system of three coplanar forces in equilibrium?
For three coplanar forces to be in equilibrium they must be concurrent (I) and their moments about any point must sum to zero (III). Equality of upward and downward forces (II) is not a general requirement unless forces are vertical only. Thus I and III are necessary and sufficient.
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Question 50
What is the frequency of vibration if the balance wheel of a wrist watch makes 90 revolutions in 25 s?
Frequency $f=$ revolutions per second $=\dfrac{90}{25}=3.6\ \text{Hz}$.
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