Physics MCQs for NEET — Practice Questions with Answers

When performing operations with significant figures, the result should have the same number of significant figures as the value with the least number of significant figures. In the expression $(2.30 + 4.70) imes 10^5$, both 2.30 and 4.70 have 3 significant figures. The sum is 7.00, which also has 3 significant figures. Therefore, the number of significant figures in the result is 3.

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].