Correct Answer: B. 7.5 x 10¹¹Nm^-2

Explanation

Young's modulus = \(\frac{F}{A}\) \(\div\) \(\frac{e}{L}\)

= \(\frac{20}{8 \times 10^{-7}}\) \(\div\) \(\frac{10^{-4}}{3}\)

= 7.5 x 10¹¹Nm^-2

Correct Answer: D. 400J

Correct Answer: B. 2.5

Correct Answer: B. uniform velocity

Correct Answer: C. 5m

Explanation

a) (i) A wave motion is a disturbance which travels through a medium and transfers energy from one point to another without causing any permanent displacement of the medium itself.

(ii) A stationary wave is a wave got when two progressive waves of equal amplitude and frequency or wavelength travelling in opposite direction are superimposed. In stationary wave nodes are pendulum of permanently at rest while antinodes are at maximum amplitude

Stationary wave along a string

(b)(i) Physical properties of wave are: diffraction, refraction, reflection and.interference.

(ii) Amplitude is the maximum displacement of a oscillating object from its equilibrium position. A node is a point on a stationary wave at zero amplitude while an antinode is a point at maximum amplitude.

(iii) Frequency of vibration on a stretch string depends on;

- Tension on the string

- Length of stretch string

- Mass per unit length and density of the string

(c) y = 5 sin (3x - 4t); y = A sin (\(\frac{2 \pi x}{\pi} \times 2 \pi ft\))

\(\frac{2 \pi x}{\pi}\) = 3x

\(\pi = \frac{2 \pi}{3}\)m = 2\(\pi ft\) = 4t

f = \(\frac{2}{\pi }\)

(i) = \(\frac{2}{\pi}\) = 0.64Hz

(ii) T = \(\frac{1}{f}\) = \(\frac{1}{0.64}\) = 1.56(s)

(iii) V = f\(\pi\) = 0.64 x \(\frac{2 \pi}{3} = 1.34\)m/s

Correct Answer: D. objective focal point coincides wih that of the eyepiece

Correct Answer: A. 10.0^oC

Explanation

100....180

A......45

0......30

\(\frac{45 - 30}{180 - 30} = \frac{A - 0}{100 - 0}\)

A = \(\frac{15 \times 100}{150} = 10^oC\)

Correct Answer: A. To prevent resonance on the bridge

Explanation

Soldiers march disorderly while crossing a bridge to prevent resonance because when soldiers march in orderly manner across a bridge, they generate a rhythmic oscillation of wave on the bridge and at a certain point, would start oscillation to the same rhythm as that of the marching steps. This oscillation would reach a maximum peak when the bridge can no longer sustain its own strength and hence collapses. So for this reasons, soldier are ordered to march disorderly while crossing a bridge.

Correct Answer: D. 151

Explanation

P = \(\frac{25}{50} = 0.5\)

V.R = \(\frac{2\pi D}{p} = \frac{2 \times 3.142 \times 12}{0.5}\)

= 151