Embibe Experts Solutions for Chapter: Physical World and Measurement, Exercise 2: Exercise-2

If in a system, the force of attraction between two point masses of $1 \mathrm{kg}$ each situated $1 \mathrm{km}$ apart is taken as a unit of force and is called Notwen (Newton written in reverse order) and if $\mathrm{G}=6.67\times {10}^{-11} \mathrm{N}-{\mathrm{m}}^2{ \mathrm{kg}}^{-2}$ in SI units then which of the following is true

If the unit of length be doubled then the numerical value of the universal gravitation constant $\mathrm{G}$ will become (with respect to present value)

Bernoulli’s equation is given by $\mathrm{p}+\frac{1}{2}{\mathrm{\rho v}}^2+\mathrm{h\rho g}=\mathrm{k}$
Where $\mathrm{p}=$ pressure, $\mathrm{\rho }=$ density, $\mathrm{v}=$ speed, $\mathrm{h}=$ height of the liquid column, $\mathrm{g}=$ acceleration due to gravity and $\mathrm{k}$ is constant. The dimensional formula for $k$ is same as that for :

When a wave travels in a medium, the displacement of a particle located at distance $x$ at time $t$ is given by $y=a\sin \left(bt-cx\right)$ where $a, b$ and $c$ are constants of the wave. The dimensions of $\frac{\mathit{b}}{\mathit{c}}$ are the same as that of

A physical quantity $\mathrm{x}$ can be dimensionally represented in terms of $\mathrm{M}, \mathrm{L}$ and $\mathrm{T}$ that is $\mathrm{x}={\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}}$. The quantity time

If the velocity of light $\mathrm{c}$ , gravitational constant $\mathrm{G}$ and Planck's constant $\mathrm{h}$ are chosen as fundamental units, then the dimensions of mass in this new system is

Calorie is a unit of heat or energy whose value is $4.2 \mathrm{J}$, where $\mathrm{J}=1 {\mathrm{kgm}}^2{ \mathrm{s}}^{-2}$. If one uses a unit system in which units of mass, length and time are taken as $\mathrm{\alpha } \mathrm{kg}, \mathrm{\beta }$ metre and $\mathrm{\gamma }$ second respectively, then the value of calorie in this system will be-

Which of the following groups have the same dimensions.