Unit 10 - Numerical Problems

10.1. The time period of a simple pendulum is 2 s. What will be its length on the Earth? What will be its length on the Moon if $g_{\mathrm{m}}=g_{\mathrm{e}}\mathrm{/}6?$$g_{\mathrm{m}} = g_{\mathrm{e}} / 6?$ where $g_{\mathrm{e}}=10\mathrm{m}{\mathrm{s}}^{-2}$$g_{\mathrm{e}} = 10 \mathrm{m} \mathrm{s}^{- 2}$ .

Ans. (1.02 m, 0.17 m)

10.2. A pendulum of length $0.99\mathrm{m}$$0.99 \mathrm{m}$ is taken to the Moon by an astronaut. The period of the pendulum is $4.9\mathrm{s}$$4.9 \mathrm{s}$ . What is the value of $g$ on the surface of the Moon?

10.3. Find the time periods of a simple pendulum of 1 metre length, placed on Earth and on Moon. The value of $g$ on the surface of Moon is $1 / 6^{\text{th}}$ of its value on Earth, where $g_{\mathrm{e}}$$g_{\mathrm{e}}$ is $10\mathrm{m}{\mathrm{s}}^{-2}$$10 \mathrm{m} \mathrm{s}^{- 2}$ .

Ans. (2 s, 4.9 s)

10.4. A simple pendulum completes one vibration in two seconds. Calculate its length, when $g=10.0\mathrm{m}{\mathrm{s}}^{-2}$$g = 10.0 \mathrm{m} \mathrm{s}^{- 2}$ .

Ans. (1.02 m)

10.5. If 100 waves pass through a point of a medium in 20 seconds, what is the frequency and the time period of the wave? If its wavelength is $6\mathrm{c}\mathrm{m}$$6 \mathrm{cm}$ , calculate the wave speed.

Ans. (5 Hz, 0.2 s, 0.3 m s $^{- 1}$ )