Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The absolute error has the same unit as the quantity itself.
Reason (R): Fractional error has no unit.
In the light of above statements, choose the correct answer from the options given below.
1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Absolute error \(\Delta x\) has the same unit as the physical quantity. Fractional error is the ratio \(\Delta x / x\) and is dimensionless (no unit). Both statements are true, but the lack of unit in fractional error does not explain why absolute error has a unit.
Assertion (A): When we change the unit of measurement of a quantity, its numerical value changes.
Reason (R): Smaller the unit of measurement smaller is its numerical value.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The physical magnitude is invariant, expressed as \(n u = \text{constant}\). Therefore, numerical value is inversely proportional to the unit size. A smaller unit leads to a larger numerical value, making R false.
Assertion (A): If the measuring instruments used are perfect, then measurements made will be perfect.
Reason (R): Measurements depend upon only on the instruments.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Even with perfect instruments, errors due to observation, environmental factors, or experimental setup can occur. Both statements are false.
Assertion (A): When an algebraic equation has been derived, it is advisable to check it for dimensional consistency.
Reason (R): This guarantees that the equation is correct.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
A dimensionally consistent equation is not guaranteed to be physically correct, as dimensionless constants cannot be verified through dimensional analysis. Thus, R is false.
Assertion (A): eV and joule are the S.I. units of energy used in modern physics and mechanics respectively.
Reason (R): Different types of energies require different units in S.I. units.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The SI unit of all forms of energy is the joule. Electron-volt (eV) is not an SI unit, and different forms of energy do not require different SI units.
Assertion (A): Pressure and energy density have same units in SI.
Reason (R): Dimensions of energy density and pressure are same.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Pressure has dimensions of \([M L^{-1} T^{-2}]\). Energy density (energy per unit volume) also simplifies to \([M L^{-1} T^{-2}]\). Since their dimensions are identical, they share the same SI units.