NEET Questions

The dimensional formula for pressure is:

Which of the following has the dimensional formula $[M^0L^0T^0]$?

What is the dimensional formula of angular velocity?

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 $k$.

The viscous force $F$ acting on a sphere moving through a liquid depends on the radius $r$ of the sphere, the velocity $v$ of the sphere, and the coefficient of viscosity $η$ of the liquid. If $F = kη^arv^b$, where $k$ is a dimensionless constant, using dimensional analysis, find the values of $a$, $b$.

If the speed $v$ of transverse waves on a stretched string depends on the tension $T$ in the string and the mass per unit length $μ$ of the string, which of the following is dimensionally consistent?

The frequency $ν$ of vibration of a stretched string depends on its length $l$, its linear mass density $μ$, and its tension $T$. Which of the following is a possible formula for $ν$, consistent with the principle of homogeneity?