2022 Physics WAEC (WASSCE) Essay Past Questions (Paper 2)

2022 Physics WAEC Theory Past Question 1

The diagram below illustrates the trajectory of a fired missile from point P at 250 ms^-1

If the missile hits point Q after 40 s, calculate the distance |PQ|

Solution:

Given: Time of flight, T = 40 s

u = 250 ms^-1

θ = 42º

|PQ| = range of projection = ?

PQ| = Range = u_x .T

u_x = u cos θ

∴| PQ|  = u cos θ  × T

= 250 cos 42 × 40

= 7431 m or 7.4 km

2022 Physics WAEC Theory Past Question 2

State three properties of an intrinsic semiconductor.

Answer:

• An intrinsic semiconductor behaves like an insulator at T=0K.
• It is a pure semiconductor i.e contain no impurities.
• Its characteristic is temperature-dependent.
• Electrical conductivity is comparatively low.
• The densityDensity is the measurement of how tightly a material is packed together i.e. how closely the particles are packed in the material. The tighter the material is packed the more its... More of electrons is equal to the density of holes.
• Are tetravalent i.e. they have four valence electrons. (Group IV element)

2022 Physics WAEC Theory Past Question 3

The effective potential energy, E, of a lunar satellite of mass, m₁ , moving in an elliptical orbit around the moon of mass, m₂ , is given by

E = \(\frac{K^2}{2m_1 r^2} = \frac{Gm_1m_2}{r}\)

where r is the distance of the satellite from the moon and G is the universal gravitational constant of dimensions, \(\scriptsize M^{-1}L^3 T^{-2}\)

Determine the dimensions of the angular momentum, K, of the satellite using dimensional analysis.

Solution:

E = \(\frac{K^2}{2m_1 r^2} = \frac{Gm_1m_2}{r}\)

∴ \(\frac{K^2}{2m_1 r^2} = \frac{Gm_1m_2}{r}\)

⇒ \(\scriptsize k^2 = \normalsize\frac{Gm_1m_2 \: \times \: 2m_1 \not{r^2}}{\not{r}}\)

⇒ \(\scriptsize k^2 = 2Gm_1m_2 m_1 \: \times \: r\)

(Note: we can ignore 2 in front of G since we are working in dimensions)

Insert Dimensions

Dimension for:
G = \(\scriptsize M^{-1}L^3 T^{-2}\)
m = M
r = L

⇒ \(\scriptsize k^2 =M^{-1}L^3 T^{-2} \: \times \: M \: \times \: M \: \times \: M \: \times \: L\)

⇒ \(\scriptsize k^2 =M^{-1} \: \times \: M^3 \: \times \: L^3 \: \times \: L \: \times \: T^{-2}\)

⇒ \(\scriptsize k^2 =M^{(-1 + 3)} \: \times \: L^{(3+1)} \: \times \: T^{-2}\)

⇒ \(\scriptsize k^2 = M^2 \: \times \: L^4  \: \times \: T^{-2}\)

⇒ \(\scriptsize k^2 = M^2  L^4  T^{-2}\)

multiply both sides by \(\frac{1}{2}\) or find the square root of both sides.

⇒ \(\scriptsize k^{2\: \times \: \frac{1}{2}} = \left(M^2  L^4  T^{-2}\right)^{\frac{1}{2}}\)

⇒ \(\scriptsize k = M^{2\: \times \: \frac{1}{2}}  L^{4\: \times \: \frac{1}{2}}  T^{-2\: \times \: \frac{1}{2}}\)

⇒ \(\scriptsize k = M  L^{2}  T^{-1}\)

∴ dimensions of the angular momentum, K, ⇒ \(\scriptsize  M  L^{2}  T^{-1}\)