Question
Convert 1 Joule of energy into CGS system.
✓
Answer
The unit of energy is SI system is Joule and that is in the CGS system is erg.
Dimensional formula of energy $=\left[ M ^1 L^2 T^{-2}\right]$
Here, $a=1, b=2, c=-2$
S.I. System
$M _1=1 kg$
$L _1=1 m$
$T _1=1 s$
$n _1=1$ Joule
C.G.S. System
$M _2=1 gm$
$L _2=1 cm$
$T _2=1 s$
$n _2=$ ?
$\begin{aligned}
n_2 & =n_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c \\
& =1\left[\frac{1 kg}{1 g}\right]^1\left[\frac{1 m}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1\left[\frac{1000 g}{1 g}\right]^1\left[\frac{100 cm}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1 \times 10^3 \times\left(10^2\right)^2=10^3 \times 10^4=10^7
\end{aligned}$
Hence, 1 Joule $=10^7$ erg.
Dimensional formula of energy $=\left[ M ^1 L^2 T^{-2}\right]$
Here, $a=1, b=2, c=-2$
S.I. System
$M _1=1 kg$
$L _1=1 m$
$T _1=1 s$
$n _1=1$ Joule
C.G.S. System
$M _2=1 gm$
$L _2=1 cm$
$T _2=1 s$
$n _2=$ ?
$\begin{aligned}
n_2 & =n_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c \\
& =1\left[\frac{1 kg}{1 g}\right]^1\left[\frac{1 m}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1\left[\frac{1000 g}{1 g}\right]^1\left[\frac{100 cm}{1 cm}\right]^2\left[\frac{1 s}{1 s}\right]^{-2} \\
& =1 \times 10^3 \times\left(10^2\right)^2=10^3 \times 10^4=10^7
\end{aligned}$
Hence, 1 Joule $=10^7$ erg.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
At, what speed will the velocity head of stream of water be 40cm?
A mass of 2kg is suspended with thread AB Thread CD of the same type is attached to the other end of 2kg mass. Lower thread is pulled gradually, harder and harder in the downward directon so as to apply force on AB. Which of the threads will break and why?
Prove that the angular momentum of a single particle moving with a constant velocity around a point remains constant throughout its motion.(NCERT)
The potential difference between the terminals of a 6.0V battery is 7.2V when it is being charged by a current of 2.0A. What is the internal resistance of the battery?
A nearsighted person cannot clearly see beyond 200cm. Find the power of the lens needed to see objects at large distances.
Explain why:
Heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water.
Heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water.
Read the following two statements below carefully and state, with reasons, if it is true or false.
(a) The Young’s Modulus of rubber is greater than that of steel;
(b) The stretching of a coil is determined by its shear modulus.
(a) The Young’s Modulus of rubber is greater than that of steel;
(b) The stretching of a coil is determined by its shear modulus.
Find the time required to liberate 1.0 litre of hydrogen at STP in an electrolytic cell by a current of 5.0A.
A pivoted aluminium bar falls much more slowly through a small region containing a magnetic field than a similar bar of an insulating material. Explain.
A proton beam is going from east to west. Is there an electric current? If yes, in what direction?