Tag: substances, objects and energy

Questions Related to substances, objects and energy

A single conservative force F(x) acts on a $1$ kg particle that moves along the x-axis. The potential energy U(x) is given by $U(x) = 10+(x-1)^2$ Where x is in meters. At x =$2$ m, the particle has a kinetic energy of $8$ Joules. Then the mechanical energy of particle is

  1. $18$ J

  2. $19$ J

  3. $20$ J

  4. $10$ J


Correct Option: A

If $484J$ of energy is spent in increasing the speed of a wheel from $60rpm$ to $360\ rpm$, the $M.I$ of the wheel is

  1. $1.6\ kg\ m^{2}$

  2. $0.3\ kg\ m^{2}$

  3. $0.7\ kg\ m^{2}$

  4. $1.2\ kg\ m^{2}$


Correct Option: C
Explanation:

$\begin{array}{l} { \eta _{ 1 } }=60rpm=\dfrac { { 60 } }{ { 60 } } rps=1rps \ \therefore { w _{ 1 } }=2r{ \eta _{ 1 } }=2\pi  \ { \eta _{ 2 } }=\dfrac { { 360 } }{ { 60 } } rpm=6rps \ { w _{ 2 } }=2\pi { \eta _{ 2 } }=12\pi  \end{array}$

484 joule of energy is spent in increasing.
$\begin{array}{l} \frac { 1 }{ 2 } Iw _{ 2 }^{ 2 }-\dfrac { 1 }{ 2 } Iw _{ 1 }^{ 2 }=484 \ \dfrac { I }{ 2 } \left( { { w _{ 2 } }+{ w _{ 1 } } } \right) \left( { { w _{ 2 } }-{ w _{ 1 } } } \right) =484 \ \dfrac { I }{ 2 } \left( { 12\pi +2\pi  } \right) \left( { 12\pi -2\pi  } \right) =484 \ I\, \, 14\pi .10\pi =484 \ I=\dfrac { { 484\times 2 } }{ { 140\times { \pi ^{ 2 } } } } =\dfrac { { 484\times 2 } }{ { 140\times 9.86 } }  \ =0.7\, \, kg\, \, { m^{ 2 } } \end{array}$
Option C.

State True or False :
Coal forms from plants. 

  1. True

  2. False


Correct Option: A
Explanation:

Coal is fossil fuel formed from remains of plants that lived and died millions of years ago.

Which is a non-renewable energy resource?

  1. coal

  2. solar

  3. tides

  4. wind


Correct Option: A
Explanation:

All fossil fuels are non- renewable source of energy. Since coal is a fossil fuel so, it is a non renewable resource.

Sound is form of

  1. Energy

  2. Matter

  3. Radiation

  4. Electromagnetic energy

  5. None of the above


Correct Option: A
Explanation:

Sound is considered as a form of energy because it obeys the First Law of Thermodynamics which states that energy can neither be created nor destroyed but it changes from one form to another. Sound energy is produced when an object vibrates. The sound vibrations cause waves of pressure that travel through a medium, such as air, water, wood or metal. Sound energy is a form of mechanical energy.

The vast amount of ses weeds present in oceans may provide an endless source of.

  1. nuclear energy

  2. methane

  3. thermal energy ocean

  4. none of these


Correct Option: B