Tag: powers

Questions Related to powers

1 yotta is ____ yocto

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

  1. $10^{48}$

  2. $10^{-48}$

  3. $10^{47}$

  4. $10^{49}$

Show answer
Correct Option: A
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

1 millimeter is ____ terameter.

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

  1. $10^{-15}$

  2. $10^{-14}$

  3. $10^{-13}$

  4. $10^{-16}$

Show answer
Correct Option: A
Explanation:

$1$ milimeter $=10^{-3}$ meter and $1$ terameter $=10^{12}$ meter

So, $1$ milimeter $=10^{-3}\times \dfrac{10^{12}}{10^{12}}$ meter $=\dfrac{10^{-3}}{10^{12}}\times 1$ terameter $=10^{-15}$ terameter 

1 nanometer is ____ centimeter.

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

  1. $10^{-8}$

  2. $10^{-7}$

  3. $10^{-9}$

  4. $10^{-6}$

Show answer
Correct Option: B
Explanation:

$1$ nanometer $=10^{-9}$ meter and $1$ centimeter $=10^{-2}$ meter

So, $1$ nanometer $=10^{-9}\times \dfrac{10^{-2}}{10^{-2}}$ meter $=\dfrac{10^{-9}}{10^{-2}}\times 1$ centimeter $=10^{-7}$ centimeter

1 MeV is equal to

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

  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

Show answer
Correct Option: D
Explanation:

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


$1 eV=1.6\times10^{-19}\ J$ 

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

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

Electron volt is the unit used to represent 

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

  1. energy

  2. power

  3. intensity

  4. charge of electron.

Show answer
Correct Option: A
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  $1.602\times 10^{-19}\,joule$.

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

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

  1. becomes 8 times

  2. becomes 16 times

  3. decrease 16 times

  4. increase 4 times

Show answer
Correct Option: B
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.

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

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

  1. 1

  2. 2

  3. -1

  4. 0

Show answer
Correct Option: D
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$
State whether true or false.
One mega watt is 10 times that of one kilowatt.
physics dynamics - explaining motion exponentiation index notation and products of prime factors powers

  1. True

  2. False

Show answer
Correct Option: B
Explanation:
Mega is a prefix used for a factor of $10^6$.
Thus  $1 \ mega \ watt = 10^6 \ watt$
So, the given statement is false.

The approximate value of ${ \left{ { { \left( 3.92 \right)  }^{ 2 }\quad +3\left( 2.1 \right)  }^{ 4 } \right}  }^{ { 1 }/{ 6 } }$

maths indices exponentiation index notation and products of prime factors powers

  1. $2.0466$

  2. $2.755$

  3. $2.345$

  4. $0.242718$

Show answer
Correct Option: A
Explanation:

${(3.92^2+3(2.1^4)}^\dfrac{1}{6}$

 
$=(15.3664+3\times19.4481)^\dfrac{1}{6}$


$=(15.3664+58.3443)^\dfrac{1}{6}$

$=(73.7107)^\dfrac{1}{6}$

$=2.0476$

If ${2}^{1998}-{2}^{1997}-{2}^{1996}+{2}^{1995}={K.2}^{1995}$, then the value of $K$ is 

maths indices exponentiation index notation and products of prime factors powers

  1. 3

  2. 2

  3. -2

  4. -3

Show answer
Correct Option: A
Explanation:
$2^{1998}-2^{1997}-2^{1996}+2^{1995}=k. 2^{1995}$
$2^{1995}(2^3-2^2-2^1+1)=k. 2^{1995}$
$(2^3-2^2-2^1+1)=k$
$(8-4-2+1)=k$
$k=3$