Units & measurements practice · Mixed difficulty

The position of the particle moving along $Y$-axis is given as $y=A t^2-B t^3$, where $y$ is measured in metre and $t$ in second. Then, the dimensions of $B$ are

The work done by a battery is $W = \varepsilon \Delta q$ , where $\Delta q$ charge transferred by battery, $\varepsilon$ = emf of the battery. What are dimensions of emf of battery?

A geometry ruler has 20 divisions between 5 cm. Its least count is

The focal length of a mirror is given by $\frac{1}{f} = \frac{1}{u} + \frac{{1\;}}{v}$ where u and $v$ represent object and image distances respectively. The maximum relative error in $f$ is

A student performs an experiment for determination of $\mathrm{g}\left( { = \frac{{4{\mathrm{\pi }^2}l}}{{{T^2}}}} \right),\mathrm{\;}l \approx 1\mathrm{m},$, and he commits an error of $\Delta l.$. For T he takes the time of n oscillations with the stop watch of least count ∆T and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate?

The SI unit of electrochemical equivalent is

The value of ${(17.5)^2}$ is

Let L denote the self-inductance of coil which is in series with a capacitor of capacitance C. Which of the following has the unit second?

If velocity of light c, acceleration due to gravity g and density d are the fundamental quantities in a system of measurement then mass has

The SI unit of gravitational potential is

If a book with many printing errors contains four different formulae for the displacement $y$ of a particle undergoing a certain periodic motion.
(1) $y=a \sin \frac{2 \pi t}{T}$
(2) $y=a \sin v T$
(3) $y=\frac{a}{T} \sin \frac{t}{a}$
(4) $y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
where $a$ is the maximum displacement of the particle, $v$ is the speed of particle, $T$ is the time period of motion. Then dimensionally

SI unit of permittivity is

If 1 g cm ${\mathrm{s}^{ - 1}} = x$ newton-second, then the number x is equal to

E, m, L and G denote energy, mass, angular momentum and gravitational constant respectively, $\frac{{E{L^2}}}{{{m^5}{G^2}}}$ has the dimensions of

The dimensional formula for impulse is same as the dimensional formula for

The number 0.004 has significant figures equal to

A physical quantity $Q$ is calculated according to the expression

$Q=\frac{A^3 B^3}{C \sqrt{D}}$

If percentage errors in $A, B, C, D$ are $2 \%, 1 \%, 3 \%$ and $4 \%$, respectively. What is the percentage error in $Q$ ?

Which of the following is the most accurate instrument for measuring length?

Dimensions of frequency are

In an experiment the angles are required to be measured using an instrument. 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

If $v = \frac{A}{t} + B{t^2} + C{t^3}$ , where $v$ is velocity, t is time and A,B and C are constants, then the dimensional formula of B is

One shake is equal to

Statement-I: If error in measurement of mass is $2 \%$ and that in measurement of velocity is $5 \%$ than error in measurement of kinetic energy is $6 \%$.
Statement-II: Error in kinetic energy is $\frac{\Delta K}{K}=\left(\frac{\Delta m}{m}+2 \frac{\Delta v}{v}\right)$

Dimensions of coefficient of viscosity are

A spherometer has 100 equal divisions marked along the periphery of its disc and one full rotation of the disc advances on the main scale by $0.01 \mathrm{~cm}$. The least count of this system is

In a simple pendulum experiment for determination of acceleration due to gravity $(\mathrm{g})$, time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be $30 \mathrm{~s}$. The length of pendulum is measured by using a meter scale of least count $1 \mathrm{~mm}$ and the value obtained is $55.0 \mathrm{~cm}$. The percentage $(\%)$ error in the determination of $g$ is close to

Energy per unit volume represents

A physical quantity $X$ is given by $X=\frac{2 k^3 l^2}{m \sqrt{n}}$

The percentage error in the measurements of $k, l, m$ and $n$ are $1 \%, 2 \%, 3 \%$ and $4 \%$, respectively. The value of $X$ is uncertain by

From the dimensional consideration, which of the following equation is correct

To measure the distance of a planet from the Earth, ______ method is used.