NEET Unit And Dimensions MCQs & PYQs

Practice NEET Unit And Dimensions Questions

Question 21:

easy

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.

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.

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Question 22:

easy

Taking into account of the significant figures, value of \(9.99\text{ m} – 0.0099\text{ m}\) is

When subtracting, the result must be rounded off to the least number of decimal places in any of the terms. Here, \(9.99\) has two decimal places, so \(9.9801\) is rounded to \(9.98\text{ m}\).

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Question 23:

easy

The pitch of a screw gauge is 1 mm and there are 100 divisions on circular scale. While measuring the thickness of a sheet, the main scale reads 1 mm and \(52^{\text{nd}}\) division on circular scale coincide with the reference line. The thickness of the sheet is

Least count \(LC = \frac{\text{Pitch}}{\text{Number of circular divisions}} = \frac{1 \text{ mm}}{100} = 0.01 \text{ mm}\). Thickness \(= \text{MSR} + \text{CSR} \times LC = 1 \text{ mm} + 52 \times 0.01 \text{ mm} = 1.52 \text{ mm} = 0.152 \text{ cm}\).

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Question 24:

easy

Dashrath measures the length of a wire using a meter scale with a least count of 1 mm and finds it to be L = 75.0 cm. He also measures diameter of thin wire using a screw gauge with a least count of 0.01 mm and finds it to be d = 0.500 cm. He uses these measurements to calculate the volume of wire. The maximum percentage error in volume of wire is nearly

Volume of wire is \(V = \pi \left(\frac{d}{2}\right)^2 L ⇒ \frac{\Delta V}{V} = 2\frac{\Delta d}{d} + \frac{\Delta L}{L} = 2\left(\frac{0.001}{0.500}\right) + \frac{0.1}{75.0} \approx 0.53%\).

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Question 25:

easy

The dimensional formula for impulse is

Impulse is given by \(I = F \cdot t = [MLT^{-2}][T] = [MLT^{-1}]\).

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Question 26:

easy

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.

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.

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Question 27:

easy

Assertion (A): If the measuring instruments used are perfect, then measurements made will be perfect.

Reason (R): Measurements depend upon only on the instruments.

Even with perfect instruments, errors due to observation, environmental factors, or experimental setup can occur. Both statements are false.

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Question 28:

easy

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.

A dimensionally consistent equation is not guaranteed to be physically correct, as dimensionless constants cannot be verified through dimensional analysis. Thus, R is false.

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Question 29:

easy

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.

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.

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Question 30:

easy

Assertion (A): Pressure and energy density have same units in SI.

Reason (R): Dimensions of energy density and pressure are same.

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.

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