A car travels from point A to B with speed 40 km/h and returns from B to A with speed 60 km/h. The average speed for the entire journey is: MCQ with Answer and Explanation
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Question #1
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A thermometer reads 25°C. What is the corresponding temperature in Kelvin?
Correct Answer: Option B
Explanation:
To convert a temperature from Celsius to Kelvin, the formula is K = °C + 273.15. For most physics problems, we use 273. Therefore, K = 25 + 273 = 298 K. Kelvin is the SI unit of temperature, and it never uses a degree symbol.
To convert a temperature from Celsius to Kelvin, the formula is K = °C + 273.15. For most physics problems, we use 273. Therefore, K = 25 + 273 = 298 K. Kelvin is the SI unit of temperature, and it never uses a degree symbol.
Question #2
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Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension.
Correct Answer: Option C
Explanation:
The coefficient of linear expansion is alpha. A cube of side L has volume V = L^3. When heated, the new length is L(1+alphadT). The new volume is [L(1+alphadT)]^3. Expanding via binomial theorem and ignoring higher-order small terms gives V' = V(1 + 3alphadT). Thus, the volume expansion coefficient gamma is equal to 3alpha. Reason R correctly explains Assertion A.
The coefficient of linear expansion is alpha. A cube of side L has volume V = L^3. When heated, the new length is L(1+alphadT). The new volume is [L(1+alphadT)]^3. Expanding via binomial theorem and ignoring higher-order small terms gives V' = V(1 + 3alphadT). Thus, the volume expansion coefficient gamma is equal to 3alpha. Reason R correctly explains Assertion A.
Question #3
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The dimensional formula of gravitational constant G is:
Correct Answer: Option D
Explanation:
From Newton's law: F = Gm₁m₂/r² ⇒ G = Fr²/(m₁m₂). Force F has [MLT⁻²], r² has [L²], m₁m₂ has [M²]. Thus G = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. Memory aid: 'G dimensions: [M⁻¹L³T⁻²]; small value (6.67×10⁻¹¹) reflects weak gravity'. This dimensional analysis question tests ability to derive constants, frequently appearing in competitive exams. Always verify by substituting into fundamental equations; dimensional consistency is a powerful tool for error checking in physics problems.
From Newton's law: F = Gm₁m₂/r² ⇒ G = Fr²/(m₁m₂). Force F has [MLT⁻²], r² has [L²], m₁m₂ has [M²]. Thus G = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. Memory aid: 'G dimensions: [M⁻¹L³T⁻²]; small value (6.67×10⁻¹¹) reflects weak gravity'. This dimensional analysis question tests ability to derive constants, frequently appearing in competitive exams. Always verify by substituting into fundamental equations; dimensional consistency is a powerful tool for error checking in physics problems.
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