Units And Measurement And Dimensions - Mechanics - Physics Previous Year Questions

In a $R$ - $C$ circuit, where $R$ is resistance and $C$ is capacitance, which of the following has the dimension of time?

The number of significant figures in $3.78 \times 10^{22} \mathrm{~kg}$ is

The efficiency of an engine is given by $\eta=\frac{\alpha \beta}{\sin \theta} \cdot \log _e \frac{\beta x}{k T}$, where $\alpha$ and $\beta$ are constants. If $T$ is the absolute temperature, $k$ is Boltzmann constant, $\theta$ is angular displacement and $x$ is distance, then the incorrect statement is

Velocities $(v)$ and accelerations (a) in two systems of units 1 and 2 are related as $v_2=\frac{n}{m^2} v_1$ and $a_2=\frac{a_1}{m n}$ respectively. Here $m$ and $n$ are constants. Dimensionally relations between distances ( $s_1$ and $s_2$ ) and times ( $t_1$ and $t_2$ ) in the two systems are respectively

A physical quantity $X$ is given by $X=\frac{2 k^3 l^2}{m \sqrt{n}}$. The percentage errors in the measurements of $k, l, m$ and $n$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The value of $X$ is uncertain by

The number of significant figures in the measurement of a length 0.079000 m is

In five successive measurements, the mass of a ball is measured to be $2.61 \mathrm{~g}, 2.58 \mathrm{~g}, 2.40 \mathrm{~g}, 2.73 \mathrm{~g}$ and 2.80 g . The absolute error in the measurement is

Due to an explosion underneath water, a bubble started oscillating. If this oscillation has time period $T$,which is proportional to $p^\alpha S^\beta E^\gamma$, where $p$ is static pressure, $S$ is density of water and $E$ is total energy of explosion. Determine $\alpha, \beta$ and $\gamma$.

Select the physical quantities in Column I and Column II having same dimensions

A physical quantity $S$ is related to four observables $a, b, c$ and $d$ as $S=\frac{\sqrt{a b}}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$ and $d$ are $2 \%, 1 \%, 1 \%$ and $1 \%$ respectively, then percentage error in the quantity $S$ is

If the velocity of light $c$, the gravitational constant $G$ and Planck's constant $h$ are chosen as the fundamental units, the dimension of density in the new system is

The dimension of angular momentum in mass $(M)$, length $(L)$ and time $(T)$ is

What is the dimension of $\frac{1}{\mu_0 \varepsilon_0}$ ? ( $\mu_0=$ magnetic permeability and $\varepsilon_0=$ permittivity of free space)

The surface tension of 70 dynes $/ \mathrm{cm}$ is equal to

The dimension of $\frac{E^2}{\mu_0}$ in mass $(M)$, length $(L)$ and time

$(T)$ is $(E=$ electric field,

$\mu_0=$ permeability of free space)

In an experiment the angles are required to be measured using an instrument in which 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half a degree $\left(=0.5^{\circ}\right)$, then the least count of the instrument is