The density of a material in $CGS$ system of units is $4\, g\, cm^{-3}$ . In a system of units in which unit of length is $10\, cm$ and unit of mass is $100 \,g,$ the value of density of material will be
- [AIPMT 2011]
- A$0.04$
- B$0.4$
- C$40$
- D$400$
Similar Questions
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.
It is estimated that per minute each $cm^2$ of earth receives about $2\ cal (1\ cal = 4.18\ J)$ of heat energy from the sun. This is called Solar constant. In $SI$ units the value is :-
Match List$-I$ with List$-II.$
List$-I$
List$-II$
$(a)$ Capacitance, $C$
$(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$
$(b)$ Permittivity of free space, $\varepsilon_{0}$
$(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$
$(c)$ Permeability of free space, $\mu_{0}$
$(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$
$(d)$ Electric field, $E$
$(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$
Choose the correct answer from the options given below
| List$-I$ | List$-II$ |
| $(a)$ Capacitance, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
| $(b)$ Permittivity of free space, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
| $(c)$ Permeability of free space, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
| $(d)$ Electric field, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
- [JEE MAIN 2021]
If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are
If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are
- [AIIMS 2017]
A neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$, where $\mu_{0}$ and $c$ are the permeability and speed of light in free space, respectively. Then,
A neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$, where $\mu_{0}$ and $c$ are the permeability and speed of light in free space, respectively. Then,
- [KVPY 2017]