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Multiple choice physics dynamics - explaining motion exponentiation index notation and products of prime factors powers

1 yotta is ____ yocto

  1. $10^{48}$
  2. $10^{-48}$
  3. $10^{47}$
  4. $10^{49}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Yotta is the largest decimal unit prefix and yocto is the smallest decimal unit prefix in the metric system. 

$1$ yotta $=10^{24}$ meter and $1$ yocto $=10^{-24}$ meter
So, $1$ yotta $=10^{24}\times \dfrac{10^{-24}}{10^{-24}}$ meter $=\dfrac{10^{24}}{10^{-24}}\times 1$ yocto $=10^{48}$ yocto

Multiple choice physics dynamics - explaining motion exponentiation index notation and products of prime factors powers

1 MeV is equal to

  1. $1.6\times 10^{13} Joules$
  2. $1.6\times 10^{13} cal.$
  3. $1.6\times 10^{13} ergs$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

An electronvolt is a unit of energy equal to the work done on an electron accelerated through a potential difference of $1$ volt.


$1 eV=1.6\times10^{-19}\ J$ 

$\therefore1\,MeV=1.6\times 10^{-19}\times10^{6}\,Joules$

$1\ MeV=1.6\times10^{-13}\ J$

Multiple choice physics dynamics - explaining motion exponentiation index notation and products of prime factors powers

Electron volt is the unit used to represent 

  1. energy

  2. power

  3. intensity

  4. charge of electron.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Electron volt, unit of energy commonly used in atomic and nuclear physics, equal to the energy gained by an electron (a charged particle carrying unit electronic charge) when the electrical potential at the electron increases by one volt. The electron volt equals $1.602\times 10^{-12}\,erg$  or  $1.602\times 10^{-19}\,joule$.

Multiple choice physics dynamics - explaining motion exponentiation index notation and products of prime factors powers

If the units of length and force are increased four times, then unit of energy will

  1. becomes 8 times

  2. becomes 16 times

  3. decrease 16 times

  4. increase 4 times
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Unit of Energy $= kg. m^2/ s^2$

Unit of Force $= kg. m/s^2$

Unit of Length $= m$

Thus, unit of energy in terms of unit of force and length is given by

Unit of Energy $= (kg. m/s^2) \times (m)$

If the units of length and force are increased by four times,

the unit of energy will be:

Unit of Energy $= (4 .kg. m/s^2) \times (4m)$

Unit of Energy $= 16 (kg. m^2/s^2)$

Therefore, if the units of length and force are increased by four times, the unit of energy will change by $16$ times.

Multiple choice physics dynamics - explaining motion exponentiation index notation and products of prime factors powers

If 1 mg $ns^{-1}$ = $10^x \mu g ps^{-1}$, then the value of x is _________.

  1. 1

  2. 2

  3. -1

  4. 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
We know that
$1\ mg=10^3\ \mu g$
$1\ ns=10^3\ ps$

Therefore, it can be written as:
$1mgn{ s }^{ -1 }={ 10 }^{ 3 }\mu gn{ s }^{ -1 }$

$ =\dfrac { { 10 }^{ 3 } }{ { 10 }^{ 3 } } \mu gp{ s }^{ -1 }$

$ ={ 10 }^{ 0 }\mu gp{ s }^{ -1 }\\ \Rightarrow x=0$