Units & measurements practice · Mixed difficulty

A quantity $x$ is given by $x\, = \,\frac{{IF{v^2}}}{{W{L^4}}}$ where, $I$ is moment of inertia, $F$ is force, $v$ is work and $L$ is length. The dimensional formula for $x$ is same as that of

The dimensions of force are

Percentage error in the measurement of mass and speed are 3% and 4% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be

Given that $\mathrm{y}=A \sin \left[\left(\frac{2 \pi}{\lambda}(c t-x)\right)\right]$, where $\mathrm{y}$ and $\mathrm{x}$ are measured in metre. Which of the following statements is true?

Universal time is based on

What is the dimensions of impedance?

The numerical value of a given quantity is

Each side of a cube is measured to be $5.402 \mathrm{~cm}$. The total surface area and the volume of the cube in appropriate significant figures are :

Which is different from others by units

Density of liquid in CGS system is $0.625\mathrm{\;\;g\;c}{\mathrm{m}^{ - 3}}.$. What is its magnitude in SI system?

The dimensional formula for velocity gradient is equivalent to

The dimensions of couple are

The unit of e.m.f. is

Which of the following expresses the most accurate measurement of length of a rod?

Which has not the same unit as other?

Which of the following is not the unit of energy

Dimensions of $\frac{1}{{{\mathrm{\mu }_0}{\mathrm{\varepsilon }_0}}}$, where symbols have their usual meanings, are

If $\mathrm{G}$ be the gravitational constant and $\mathrm{u}$ be the energy density then which of the following quantity have the dimension as that the $\sqrt{\mathrm{uG}}:$

Velocity $v$ is given by $v=a t^2+b t+c$, where $t$ is time. What are the dimensions of $a, b$ and $c$, respectively?

The length of a cube is $2.1 \times {10^{ - 2}}m$. the volume in significant figures will be

Assertion: If $x$ and $y$ are the distances along $x$ and $y$ axes respectively then the dimensions of $\frac{d^3 y}{d x^3}$ is $\left[M^0 L^{-2} T^0\right]$
Reason: Dimensions of $\int\limits_{0}^b y d x$ is $\left[{M}^0 {L}^2 {T}^0\right]$

Which of the two have same dimensions

The SI unit of length is the metre. Suppose we adopt a new unit of length which equal x metre. The area of $1{m^2}$ expressed in terms of the new unit has a magnitude

The Martians use force (F), acceleration (A) and time (T) as their fundamental physical quantities. The dimensions of length on Martians system are

How many wavelengths of $K{r^{86}}\mathrm{\;}$ are there in one metre

A student writes four different expressions for the displacement $y$ in a periodic motion as a function of time $t, a$ as amplitude, $T$ as time period. Which of the following can be correct?

The division of energy by time is X. The dimensional formula of X is same as that of

Which is wrong dimension

Assertion: Surface tension and surface energy have the same dimensions.

Reason: Because both have the same S.I. unit

In the context of accuracy of measurement and significant figures in expressing results of experiment, which of the following is/are correct
(1) Out of the two measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy
(2) If one travels 478 km by rail and 397 m by road, the total distance travelled is 478 km