NEET Physics Units And Measurement Priniciple Of Homoginity MCQs

A hypothetical equation is given as $\rho = a \sqrt{P} + bT^2$, where $\rho$ is density, $P$ is pressure, and $T$ is temperature. The dimensions of $\frac{a}{b}$ are:

The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}} + kx$, where $l$ is the length, $g$ is acceleration due to gravity, and $x$ is displacement. The dimensions of $k$ are:

The velocity of a wave is given by $v = \sqrt{\frac{T}{\mu}} + ax^2$, where $T$ is tension, $\mu$ is linear density, and $x$ is displacement. What are the dimensions of $a$?

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv + kr^2v^2$. The dimensions of $k$ are:

Given the equation $P = \frac{a}{V} - \frac{b}{V^2} + cT$, where $P$ is pressure, $V$ is volume, and $T$ is temperature. What are the dimensions of $abc$?

A highly advanced alien civilization uses a unit of mass called a 'glorp' and a unit of length called a 'blarp'. Their fundamental unit of time is the 'zorp'. They discover a fundamental law of physics relating force (F), mass (m), length (l), and time (t) expressed as $F = K m^a l^b t^c$, where K is a dimensionless constant. If the dimensions of force in their system are glorp\cdot blarp \cdot zorp^{-2}$, what are the values of a, b, and c?

The time period ($T$) of a simple pendulum depends on its length ($l$) and acceleration due to gravity ($g$). Which of the following is dimensionally consistent with the principle of homogeneity?

If the velocity ($v$), acceleration ($a$), and time ($t$) are related by an equation $v = at + bt^2$, what are the dimensions of $b$?

Which of the following equations is dimensionally incorrect according to the principle of homogeneity?

The period $T$ of oscillation of a spring-mass system depends on the mass $m$ and the spring constant $k$. Using dimensional analysis and the principle of homogeneity, determine the relationship between $T$, $m$, and $k$.