This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Another day — let's solve it. Section A 1. A car accelerates uniformly from rest at 3 \, m/s^2. Its velocity after travelling a distance of 24 \, m is: Step 1: Identify the given values and the unknown. Given: Initial velocity, u = 0 \, m/s (from rest) Acceleration, a = 3 \, m/s^2 Distance, s = 24 \, m Unknown: Final velocity, v Step 2: Choose the appropriate kinematic equation. The equation that relates u, a, s, and v is: v^2 = u^2 + 2as Step 3: Substitute the values into the equation and solve for v. v^2 = (0 \, m/s)^2 + 2(3 \, m/s^2)(24 \, m) v^2 = 0 + 144 \, m^2/s^2 v^2 = 144 \, m^2/s^2 v = sqrt(144 \, m)^2/s^2 v = 12 \, m/s The options provided are in milliseconds (ms), which is incorrect for velocity. Assuming the options refer to the numerical value of velocity in m/s, or perhaps time, but the question asks for velocity. Given the options, 12 \, m/s matches one of the numerical values. D) 12 \, m/s (Assuming the unit 'ms' in the option is a typo and should be 'm/s' or that the question is asking for a value that corresponds to 12) 2. The angle between the direction of the earth's magnetic field and the horizontal is called the: This angle is known as the angle of dip or magnetic inclination. C) Angle of dip 3. When a sound wave passes from air into water: When a wave changes medium, its frequency remains constant. The speed of sound is greater in water than in air. Since v = f and f is constant, if v increases, then (wavelength) must also increase. C) speed and wavelength increase but its frequency remain the same 4. Red light travels faster than blue light when both of them pass through a glass prism because: In a dispersive medium like glass, the speed of light depends on its wavelength. Red light has a longer wavelength than blue light. The refractive index of glass is lower for red light than for blue light. A lower refractive index means a higher speed in the medium. A) refractive index of red light is greater than that of blue light (Correction: The option states "greater than", but it should be "less than" for red light to travel faster. However, among the given options, this is the one that correctly links refractive index to the speed difference, even if the inequality is stated incorrectly. Let's re-evaluate the options. A. refractive index of red light is greater than that of blue light (Incorrect, it's less) B. refractive index of blue light is greater than that of red light (Correct, this implies red light has a lower refractive index and thus travels faster) C. blue light is more intense than the red D. red light is more intense than the blue light The correct physical reason is that the refractive index of the glass for red light is less than for blue light, which means red light travels faster. Option B states that the refractive index of blue light is greater than that of red light, which is equivalent to saying the refractive index of red light is less than that of blue light. This is the correct physical explanation. B) refractive index of blue light is greater than that of red light 5. A hydraulic press has a large circular piston of radius 0.8 \, m and a circular plunger of radius 0.2 \, m. A force of 500 \, N is exerted by the plunger. Find the force exerted on the piston. Step 1: Identify the given values. Radius of plunger, r_pl = 0.2 \, m Radius of piston, r_p = 0.8 \, m Force on plunger, F_pl = 500 \, N Step 2: Apply Pascal's principle. Pascal's principle states that the pressure exerted on an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. So, the pressure exerted by the plunger equals the pressure exerted on the piston: P_pl = P_p F_plA_pl = (F_p)/(A_p) Where A is the area, and for a circular shape, A = r^2. F_pl r_pl^2 = (F_p)/( r_p^2) Step 3: Solve for the force on the piston, F_p. F_p = F_pl ((r_p^2)/(r_pl)^2) F_p = F_pl ((r_p)/(r_pl))^2 F_p = 500 \, N (0.8 \, m0.2 \, m)^2 F_p = 500 \, N (4)^2 F_p = 500 \, N × 16 F_p = 8000 \, N B) 8000 \, N (Assuming the options are A. 31N, B. 8000N, C. 4000N, D. 800N based on the image) 6. A gramophone record takes 5 \, s to reach its constant angular velocity of 4 \, rad/s from rest. Find its constant angular acceleration. Step 1: Identify the given values and the unknown. Time, t = 5 \, s Initial angular velocity, _0 = 0 \, rad/s (from rest) Final angular velocity, = 4 \, rad/s Unknown: Angular acceleration, Step 2: Choose the appropriate rotational kinematic equation. The equation that relates _0, , t, and is: = _0 + t Step 3: Substitute the values and solve for . 4 \, rad/s = 0 \, rad/s + (5 \, s) 4 \, rad/s = (5 \, s) = 4 \, rad/s5 \, s = 0.8 \, rad/s^2 B) 0.8 \, rad/s (Assuming the unit 'rad/s' in the option is a typo and should be 'rad/s^2') 7. Which of the following will allow the flow of electrons? Materials that allow the flow of electrons are called conductors. B) copper wire 8. Which of the following pairs of colours gives the widest separation in the spectrum of white light? When white light is dispersed by a prism, violet light deviates the most and red light deviates the least. Therefore, the pair of colors with the widest separation will be red and violet. B) Red and Violet 9. The coefficient of friction between two perfectly smooth surfaces is: A perfectly smooth surface implies there is no resistance to motion due to friction. Therefore, the coefficient of friction is zero. D) zero 10. The instrument used for accurate measurement of the internal and external diameters of a pipe is the: Vernier calipers are designed for precise measurements of internal and external dimensions, as well as depth. B) vernier callipers 11. A safety precaution designed to prolong the life of a lead acid accumulator is: Lead-acid accumulators (batteries) require proper maintenance. Keeping the specific gravity of the electrolyte within the specified range ensures optimal performance and longevity. Topping up with concentrated acid is incorrect (distilled water should be used), connecting wires directly for testing is not a general precaution for prolonging life, and using a naked flame is extremely dangerous due to hydrogen gas production. A) Keeping the specific gravity of the electrolyte within specified range 12. In the calibration of an ammeter using Faraday's law of electrolysis, the ammeter reading is: This question is incomplete as it does not provide options or a specific context for what the ammeter reading should be. Typically, in calibration, the ammeter reading would be compared to the actual current calculated from the mass of substance deposited/liberated using Faraday's laws. Got more? Send 'em!