NEET Questions

Which limitation of dimensional analysis prevents it from deriving the complete formula for the viscous force on a sphere moving through a fluid, given that the force (F) depends on the radius (r) of the sphere, its velocity (v), and the fluid's viscosity ($\eta$)?

A student uses dimensional analysis to analyze the time ($au$) it takes for a capacitor (C) to discharge through a resistor (R). They correctly identify that $au$ depends on R and C. However, they are unable to derive the precise relationship $au = RC$. What limitation of dimensional analysis explains this?

The density of a substance is measured as $1.234 imes 10^2$ kg/m$^3$ using instruments with precisions of 2% and 5% for mass and volume respectively. What is the correct representation of the density including error?

A student measures the length of a rod as 25.00 cm using a vernier caliper with a least count of 0.01 cm. The student then uses a meter scale with a least count of 0.1 cm to measure the same rod. Which statement is true regarding the significant figures in these measurements?

The value of $\frac{4.0 imes 10^{-2} imes 0.00302}{200.0}$ expressed with the correct number of significant figures is:

A student performs an experiment and obtains a value of $g = 9.7542 m/s^2$. The standard value is $g = 9.8 m/s^2$. Which of the following represents the student's result with the correct number of significant figures, considering the precision of the standard value?

Two students, A and B, measure the length of a table. Student A reports the length as $2.350 \pm 0.001$ m, and student B reports it as $2.35 \pm 0.01$ m. Which student's measurement is more precise, and what is the relative uncertainty in the more precise measurement?

A student performs an experiment to determine the density of a rectangular block. They measure the length as $12.12 ext{ cm}$, the width as $5.3 ext{ cm}$, and the height as $1.21 ext{ cm}$. The mass is measured as $50.2 ext{ g}$. The student calculates the volume and then the density. Which of the following correctly expresses the final calculated density with the appropriate number of significant figures?

The value of Avogadro's number is $6.02214076 imes 10^{23}$ $mol^{-1}$. A student experimentally determines Avogadro's number to be $6.022141 imes 10^{23}$ $mol^{-1}$. When reporting this value with the correct number of significant figures reflecting the precision of the experimental result, the student should report:

The mass of an electron is approximately $9.1093837 imes 10^{-31}$ kg. If this value is multiplied by the speed of light squared ($c^2 = (2.99792458 imes 10^8 m/s)^2$), what is the correct representation of the resulting energy in joules, considering significant figures?