The force $F$ acting on a body of density $d$ is related by the equation $F=\frac{y}{\sqrt{d}}$. The dimensions of $y$ are:

If the unit of force is $100\,N$,unit of length is $10\,m$ and unit of time is $100\,s$,what is the unit of mass in this system of units?

$1$ joule of energy is to be converted into a new system of units in which length is measured in $10 \,m$,mass in $10 \,kg$,and time in $1 \,minute$. The numerical value of $1 \,J$ in the new system is:

The $SI$ unit of energy is $J = kg \, m^{2} \, s^{-2}$; that of speed $v$ is $m \, s^{-1}$ and of acceleration $a$ is $m \, s^{-2}$. Which of the formulae for kinetic energy $(K)$ given below can you rule out on the basis of dimensional arguments ($m$ stands for the mass of the body):
$(a)$ $K = m^{2} v^{3}$
$(b)$ $K = (1/2) m v^{2}$
$(c)$ $K = m a$
$(d)$ $K = (3/16) m v^{2}$
$(e)$ $K = (1/2) m v^{2} + m a$

From the dimensional consideration,which of the following equations is correct?

If speed $(V)$,acceleration $(A)$,and force $(F)$ are considered as fundamental units,the dimension of Young's modulus will be