2007 - JAMB Physics Past Questions and Answers - page 4

The fundamental frequency is related to tension as
F ∝ √T

=>	F	= K
√T

∴	F1	=	F2	=>	250	=	500
√T1	√T2	√400	√T2

Since the cells are connected in parallel the net e.m.f is that of one cell, E.
However the effective internal resistance should be added as parallel resistance.
=> ¹/_v + ¹/₂₅ + ¹/₂₅ + ¹/₂₅ = 1.2
∴ v = 0.83Ω
∴ Effective e.m.f and internal resistance are respectively = 1.5V and 0.83Ω

Period is the time to complete one cycle of 360^o
=> Periodic Time T ≡ 1 cycle of 360^o
∴ ^T/₄ = ³⁶⁰/₄ = 90^o
∴ Instantaneous e.m.f E = E^o sin ωt
= E^o sin 90
But sin 90 = 1: => E = E^o x 1
= E^o

The decay process illustrated above shows that the lost β -particle to decay to the X by increase its atomic number ( from 92 to 93) and leaving the mass no. unaffected. There after, x decayed by -α emission to give Y, by decreasing the mass no. by 2 ( from 93 to 91).
Thus , the emission is β and α particles respectively

The inductive reactance is given as
Xl = 2πfl
= 2 x ⁵⁰/_π x 0.1
= 10Ω
Again from ohms law,
R = ^V/_I = ⁷⁵/_1.5 = 50Ω
∴ Thus the inductive reactance and the resistance are respectively 10Ω, and 50Ω

From faradays law, M = itz
But mass, M = volume x density
and volume = cross sectional area x thickness
M = 118.8cm² x 10^-6 x 9 x 10³
∴ 118.8cm² x 10^-6 x 9 x 10³ = 10 x t x 3.3 x 10^-7
∴ (118.8 x 9) x 10^-7 = 10 x t x 3.3 x 10^-7

∴ t = \(\frac{118.8 \times 9}{ 3.3}\)

t = 324 seconds

Convert to minutes by dividing by 60

t = \(\frac{324}{60}\)

t = 5.4 sec

Efficiency = \( \frac{W(120N)INPUT}{WORK OUTPUT} \times \frac{100}{1} \)

And for incline plane

V.R =\( \frac{1}{Sin\theta} \\ = V.R = \frac{1}{Sin30} =\frac{1}{0.5} = 2 \\
\text{therefore } \frac{60}{120} = \frac{M.A}{2}
=M.A = \frac{120}{100} = 1.2\\
\text{but M.A } = \frac{load}{effort} = \frac{120}{E}\\
\text{therefore} \frac{120}{E} = 1.2 \\
= E =\frac{120}{1.2 } = 100N \ \)


Therefore Effort up the plane = 100N

from hooke's law F=Ke
\(
\frac{F_1}{e_1} - \frac{F_2}{e_2} \text{therefore}

\frac{4}{0.02} = \frac{15}{e_2} \)

e₁ = \( \frac{0.02 x 15}{4} = 0.075M \)

The new length of the string is 4 + 0.075
= 4.075
= 4.08

Mathematically Boyle's law = PV = K
Where P = Pressure
and V = Volume


By definition Pressure = \( \frac{F}{A} = \frac{F}{M \times M} \)

Again Workdone = force x displacement

therefore \( PV = \frac{F}{A} \times V = \frac{F}{M^2} \times \frac{M^3}{1} \\
PV = \frac{F}{x\times x} \times \frac{x \times x \times x}{1} = F \times x \)

= force x displacement