NEET Questions

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 dimensional formula of gravitational potential is:

The dimensions of Planck's constant are the same as those of:

If the velocity (v), acceleration (a), and time (t) are chosen as fundamental quantities, the dimensional formula for force is:

Which of the following quantities is dimensionless?