2000 - JAMB Physics Past Questions and Answers - page 4

Inductive reactance is given by

X_L = W_L = 2πfL

X_L = 2 x π x (50/π) x 2

X_L = 200Ω

Efficiency = Output/input x 100/1

Efficiency = 3/(3+1) x 100/1

= 3/4 x 100/1 = 75%

The force on the conductor is maximum when the conductor lies perpendicular to the field during which the maximum force is given as;

F = ILB = 0.8 x 2 x 0.5 = 0.8N

For a photoemitted electron,

eV = K.E._max, where V = stopping potential and K.E. = maximum kinetic energy of the photo emitted electron given by K.E. = Energy of incident rad - Work - function

= 5ev - 3ev = 2ev

∴ eV = 2eV

V = 2eV/e = 2V

∴ Stopping Potential = 2.0V

The velocity V = 10 + 2t²

But acceleration, a = dv/dt

thus if V = 10 + 2t²

dv/dt = 4t

And t = 5s then a = 4x5 = 20m/s²

∴a = 20ms

For a simple pendulum, the period T = 2π

√  ¹/_g 

Since g, 2 and π are constant, => T ∝ √l

∴ T = K√l

Let the original length = l

thus for the length l, period T = 17s

∴ 17 = K√1 .................. [1]

Again, for the new length [1 - 1.5]

the period T = 8.5s
∴ 8.5 = k

√ [1-1.5] ...............[2]

thus dividing eqn [1] by eqn[2] we have
¹⁷/_8.5 = √(l/l-1.5)

∴2 = √(l/l-1.5)

=>4 = (l/l-1.5)

∴l = 4[l-1.5]

= 4l - 6.0

∴4l - l = 6.0

3l = 6.0

l = 2.0m

For a vibrating sonometer wire, the frequency

F = ^l/_2l √(^T/_m)

and if the length, l and mass per unit length, m, are constant, then F_o ∝ √T => F_oK√T or ^F_o/_√T = K

=> ^F_1o/_√F1 = ^F_2o/_√F2

∴ ^F_1o/_√T1 = ^F_2o/_√T2

=

∴F₂ = F_o x √2 = F_ox√2

The general wave equation is given by Y = sin A ^2π/_λ [x - vt]

= Sin A [(2π X)/λ - (2π vt)/λ]

thus if A = 0.15;λ = 0.01m; f = 550Hz

then V = f x λ = 550 x 0.01 = 5.50m/s

∴ Y = 0.15 sin [(2 x λ x X)/0.01 - (2 x λ x 5.5t)/0.01]

= 0.15 sin[200λX - 200 x λ x 5.5t]

∴ Y = 0.15 sin 200λ[x - 5.5t]

For transverse wave on string

velocity V = √^T/_M

where T is the tension, and M is the mass per unit length

∴ for T = 12N and M = 3.0 x 10^-2kgm^-1
V=

√ 12 / (3.0x10^-2 

=

√ 12 / 0.03 

=

√ 1200 / 3 

=

√ 1200 / 3 = 20

∴V = 20m/s