The determination of the value of acceleration due to gravity ($g$) by simple pendulum method employs the formula, $g = 4\pi^2 \frac{L}{T^2}$. The expression for the relative error in the value of $g$ is:

In an experiment, four quantities $a$, $b$, $c$ and $d$ are measured with percentage error $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows: $P=\frac{a^3b^2}{cd}$. Percentage error in $P$ is:

Dimensional formula for volume elasticity is

The velocity $v$ of a particle at time $t$ is given by $v = at + \frac{b}{t+c}$, where $a$, $b$ and $c$ are constants. The dimensions of $a$, $b$ and $c$ are respectively:

Which one has the dimensions different from the remaining three?

Taking into account the significant figures, what is the value of $9.99\text{ m} - 0.0099\text{ m}$?

Of the following quantities, which one has dimensions different from the remaining three?

If the unit of length and force be increased four times, then the unit of energy is:

Which of the following pairs of physical quantities has the same dimensions?