Physics 2010 Jamb Examination

For a galvanometer to be converted into a voltmeter, a high resistance \( R \) is connected in series with it. The total resistance required is given by \( R_{total} = V/I \).
Given full-scale deflection current \( I = 10 \; \text{mA} = 0.01 \; \text{A} \) and full-scale voltage \( V = 5 \; \text{V} \):\[R_{total} = \dfrac{V}{I} = \dfrac{5}{0.01} = 500\; \Omega\]\[R_{series} = R_{total} - R_g\]\[R_g = \dfrac{V_g}{I} = \dfrac{0.01 \times R_g}{0.01}\]\Since the question asks for the galvanometer resistance, for a 10 mA galvanometer to read 5 V full-scale, the internal resistance must be 10 Ω to maintain sensitivity. The remaining resistance will be added externally to make up 500 Ω.

The total inductance \( L_T \) of inductors in series is the sum of their individual inductances:\[L_T = L_1 + L_2 = 5\,\text{mH} + 15\,\text{mH} = 20\,\text{mH} = 0.02\,\text{H}\]The energy stored in an inductor is given by \( E = \dfrac{1}{2} L I^2 \).
Substituting the values:\[E = \dfrac{1}{2} \times 0.02 \times (5)^2\]\[E = 0.01 \times 25 = 0.25\,\text{J}\]\Hence, none of the options provided is correct since the correct value is 0.25 J, which is not listed.

When sound waves are reflected repeatedly by obstacles such as buildings, trees, or clouds, they reach the ear at slightly different times, causing the sound to persist after the source has stopped producing it. This persistence of sound is known as reverberation. It occurs because reflected waves overlap with the original sound waves, making the sound last longer than usual. Reverberation is commonly experienced during thunderstorms when sound waves bounce off clouds and the ground.

In the human eye, the retina is the light-sensitive layer that receives images and sends visual information to the brain. Similarly, in a camera, the photographic film (or image sensor in a digital camera) captures light and records the image. The film corresponds to the retina because both perform the same function of converting light into a form that can be interpreted—chemical in film and neural in the retina.

When ice melts in water, it converts into liquid water of exactly the same volume that it displaced while floating. This is because the ice displaces a weight of water equal to its own weight. As a result, when the ice melts completely, the water produced occupies exactly the same volume as the displaced water. Therefore, the level of water remains unchanged. The misconception that it drops arises from ignoring the principle of flotation, which ensures volume compensation.

During the night, the temperature of the air near the ground drops due to radiation of heat from the earth’s surface. When the temperature falls to the dew point, the water vapour in the air condenses into small droplets of liquid water on cool surfaces such as grass, leaves, or car roofs. These droplets are called dew. It forms directly from vapour without the need for cloud formation, differentiating it from fog or mist.

A saturated vapour occurs when the rate of evaporation of the liquid equals the rate of condensation of vapour back into the liquid. At this point, a dynamic equilibrium is established between the two processes, and the vapour exerts a definite pressure known as the saturated vapour pressure. This balance means that the number of molecules leaving the liquid surface equals the number returning, with no net change in mass or concentration.

Using the ideal gas law:\[PV = nRT\]Given: \(n = 1\,\text{mol},\; V = 10^{-2}\,\text{m}^3,\; T = 27 + 273 = 300\,\text{K},\; R = 8.3\,\text{J mol}^{-1}\text{K}^{-1}\)
Substituting:\[P = \dfrac{nRT}{V}\]\[P = \dfrac{1 \times 8.3 \times 300}{10^{-2}}\]\[P = \dfrac{2490}{0.01} = 2.49 \times 10^5\,\text{N/m}^2\]\Therefore, the pressure of the gas is \(2.49 \times 10^5\,\text{N/m}^2\).

Radiation is the transfer of heat through electromagnetic waves, and its rate depends on several factors such as the nature of the surface (e.g., rough or polished), the surface area, and the temperature difference between the emitting and absorbing bodies. Density, however, does not influence radiation because it does not affect the emission or absorption of radiant energy. It mainly affects conduction and convection, not radiation.

A density bottle is designed to determine the relative density of liquids and solids, including powdered substances. When used with a beam balance, it allows for precise determination of the weight of the substance and the volume it displaces. By comparing this with the weight of an equal volume of water, the relative density can be accurately calculated. Eureka cans, pipettes, and burettes are not suitable for this precision measurement.