Tag: dynamics - explaining motion

Questions Related to dynamics - explaining motion

A calorie is a unit of heat energy and its value is 4.18 J where $1 J = 1 kg m^2 s^{-2}$. Suppose we use a new system of units in which unit of mass equals $\alpha$ kg, the unit of length equals $\beta$ m and the unit of the time is $\gamma$ sec. Then the value of a calorie in the new system of units is then

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

  1. 4.18 $\displaystyle \frac{\gamma^2}{\alpha \beta^2}$

  2. 4.18 $\displaystyle \frac{\alpha \beta^2}{\gamma^2}$

  3. 4.18 $\displaystyle \frac{\gamma^2}{\alpha}$

  4. 4.18 $\displaystyle \frac{\beta^2}{\alpha \gamma^2}$

Show answer
Correct Option: A
Explanation:

$1 J = (1 kg) ( 1 m)^2 (1 sec)^{-2}$
$1 x = (\alpha kg) (\beta m)^2 (\gamma sec)^{-2}$
$\displaystyle \therefore \frac{1 J}{1x} = \left( \frac{1}{\alpha} \right) \left( \frac{1}{\beta} \right)^2 (\gamma)^2 = \frac{\gamma^2}{\alpha \beta^2} $
$\displaystyle \therefore 1 J = \frac{\gamma^2}{\alpha \beta^2}$ or $\displaystyle 1 cal = 4.18 \displaystyle \frac{\gamma^2}{\alpha \beta^2}$

1 fermi is equal to 

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

  1. $\displaystyle { 10 }^{ -15 }$m

  2. $\displaystyle { 10 }^{ 15 }$m

  3. $\displaystyle { 10 }^{ -12 }$m

  4. $\displaystyle { 10 }^{ 12 }$m

Show answer
Correct Option: A
Explanation:
Fermi is used to express length.
$1 \ $ fermi $= \ 10^{-15} \ m$

1 m is equal to

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

  1. $\displaystyle { 10 }^{ -6 }$ micron

  2. $\displaystyle { 10 }^{ 6 }$ micron

  3. $\displaystyle { 10 }^{ -3 }$ micron

  4. $\displaystyle { 10 }^{ 3 }$ micron

Show answer
Correct Option: B
Explanation:
$1 \ m = 10^6 \ \mu m$
$1 \ m$ is equal to $10^6$ micron.

One micron is equal to 

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

  1. $10^6 m$

  2. $10^3 m$

  3. $10^{-6} m$

  4. $10^{-3} m$

Show answer
Correct Option: C
Explanation:

One micron is equal to $10^{-6} m $. It is used for measuring micro level things. 

1 attometer is ___ nanometer.

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

  1. $10^{-9}$

  2. $10^{-8}$

  3. $10^{-7}$

  4. $10^{9}$

Show answer
Correct Option: A
Explanation:

$1$ nanometer $=10^{-9}$ meter and $1$ attometer $=10^{-18}$ meter

So, $1$ attometer $=10^{-9}\times 10^{-9}$ meter $=10^{-9}$ nanometer

1 micro ___ decameter.

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

  1. $10^{-6}$

  2. $10^{-7}$

  3. $10^{-9}$

  4. $10^{-8}$

Show answer
Correct Option: B
Explanation:

$1$ micrometer $=10^{-6}$ meter and $1$ decameter $=10$ meter

So, $1$ micrometer $=\dfrac{10^{-6}}{10}\times 10$ meter $=\dfrac{10^{-6}}{10}$ decameter $=10^{-7}$ decameter

1 picometer is ___  centimeter.

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

  1. $10^{-8}$

  2. $10^{-9}$

  3. $10^{-10}$

  4. $10^{10}$

Show answer
Correct Option: C
Explanation:

$1$ picometer $=10^{-12}$ meter and $1$ centimeter $=10^{-2}$ meter

So, $1$ picometer $=10^{-10}\times 10^{-2}$ meter $=10^{-10}$ centimeter

1 millimeter ___ picometer.

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

  1. $10^{9}$

  2. $10^{-9}$

  3. $10^{8}$

  4. $10^{10}$

Show answer
Correct Option: A
Explanation:

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

So, $1$ picometer $=10^{-9}\times 10^{-3}$ meter $=10^{-9}$ milimeter
So, $1$ milimeter $=10^9$ picometer

1 decimeter is ___ megameter.

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

  1. $10^{-7}$

  2. $10^{-6}$

  3. $10^{-5}$

  4. $10^{-8}$

Show answer
Correct Option: A
Explanation:

$1$ decimeter $=10^{-1}$ meter and $1$ megameter $=10^{6}$ meter

So, $1$ decimeter $=10^{-1}\times \dfrac{10^6}{10^6}$ meter $=\dfrac{10^{-1}}{10^6} $ megameter $=10^{-7}$ megameter

1 micrometer is ____ kilometer.

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

  1. $10^{-9}$

  2. $10^{-8}$

  3. $10^{-10}$

  4. $10^{8}$

Show answer
Correct Option: A
Explanation:

$1$ micrometer $=10^{-6}$ meter and $1$ kilometer $=10^{3}$ meter

So, $1$ micrometer $=10^{-6}\times \dfrac{10^3}{10^3}$ meter $=\dfrac{10^{-6}}{10^3}\times 1$ kilometer $=10^{-9}$ kilometer