Units & measurements practice · Mixed difficulty

A physical quantity is measured and its value is found to be nu where where n= numerical value and u= unit. Then which of the following relations is true

A cube has numerically equal volume and surface area. The volume of such a cube is

Which of the following sets of quantities have same dimensional formula?

Which of the following is not the unit of time?

The difference between the true value and measured value is called

The unit of L/R is (where L=inductance and R= Resistance)

The dimension of stopping potential ${V_0}$ in photoelectric effect in units of Planck’s constant $h,$ speed of light $c$ and gravitational constant $G$ and ampere $A$ is

The damping force on an oscillator is directly proportional to the velocity. The unit of the constant of proportionality is

An atomic clock makes use of

The dimension of torque is

In gas equation $\left( {P + \frac{a}{{{V^2}}}} \right)\left( {V - b} \right) = RT$, where T is absolute temperature, P is the pressure and V is the volume of the gas. The dimensional formula of $\left( {\frac{a}{{{V^2}}}} \right)$ is

The dimensions of electric dipole moment are

Zero error in an instrument is a

The dimensions of universal gas constant is

Assertion : Avogadro’s number is the number of atoms
in one gram mole.
Reason : Avogadro’s number is a dimensionless constant.

Which physical quantities have the same dimension

In an experiment, to measure the height of a bridge by dropping stone into water underneath, if the error in measurement of time is 0.1s at the end of 2s, then the error in estimation of height of bridge will be

The reverberation period T of a room depends on its volume V, its surface area A and velocity of sound C. If K is dimensionless constant then T =

If the error in the measurement of the volume of a sphere is 4.5%, then error in the measurement of its surface area is

The unit of surface tension in SI system is

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right].$ If $b=3$, the value of $c$ is

The dimensional formula for magnetic flux is

If E,M,L and G denote energy, mass, angular momentum and gravitational constant respectively, then the quantity $\left( {E{L^2}/{M^5}{G^2}} \right)$ has the dimensions of

Statement-I: If a physical quantity has a unit, it must not be dimensionless.
Statement-II: No physical quantity exists which has dimension but no unit.

Assertion : Number of significant figures in 0.005 is one and that in 0.500 is three
Reason : This is because zeros are not significant.

The energy (E), angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck’s constant (h) is

The pair having the same dimensions is

A gas bubble from an explosion under water oscillates with a time period T, depends upon static pressure p, density of water $\rho$ and the total energy of explosion E. Find the expression for the time period T.(where, k is a dimensionless constant)

If K denotes coefficient of thermal conductivity, d the density and c the specific heat, the unit of X, where X=K/dc will be

Zero error is a/an