Measurement MCQs for NEET — Physics Questions with Answers

The radius of the circle is 1.26 cm, which has 3 significant figures. When calculating the area using the formula $A = ext{πr}^2$, we must ensure the result is expressed with the same number of significant figures as the radius. $A = ext{π} imes (1.26)^2 ightarrow A ≈ 4.9850 cm^2$. Rounding this to 3 significant figures, we get $4.98 cm^2$.

When performing addition or subtraction in significant figures, the result should be rounded to the least number of decimal places of any number in the operation. Here, A has three decimal places (3.331 cm) and B has one decimal place (3.3 cm). So, the result should be rounded to one decimal place. Thus, A + B = 3.331 cm + 3.3 cm = 6.631 cm, rounded to one decimal place, which is 6.6 cm.

When subtracting measurements, the absolute uncertainties are added. So, the difference in lengths is (5.68 cm - 2.35 cm) with the uncertainty being (0.01 cm + 0.01 cm). This gives the result as (3.33 ± 0.02) cm.

Acceleration is defined as the change in velocity per unit time. The dimensions of velocity are [L][T]^{-1}, so the dimensions of acceleration are [L][T]^{-2}. Since mass is not involved in the dimensions of acceleration, it has a dimension of 0 for mass. Therefore, the dimensions are 0 for mass, 1 for length, and -2 for time.

Thermal conductivity (k) has the dimensional formula $ M^1 L^1 T^{-3} K^{-1} $. This represents the amount of heat conducted per unit time per unit area per unit temperature gradient.

The dimensional formula for resistance (R) is derived from Ohm's law, V = IR, where V is voltage, I is current, and R is resistance. Voltage (V) has the dimensional formula [ML^2T^-3A^-1], and current (I) has the dimensional formula [A]. Therefore, resistance (R) has the dimensional formula [ML^2T^-3A^-2].

Conductance (G) is the reciprocal of resistance (R). Since the dimensional formula for resistance (R) is [ML^2T^-3A^-2], the dimensional formula for conductance (G) will be the reciprocal of that, which is [M^-1L^-2T^3A^2].