Tag: alternative fuels and energy sources

Questions Related to alternative fuels and energy sources

A proton and a deutron both enter in a region uniform magnetic field B, moving at right angles to the field $\vec { \mathrm { B } }$  . If the radius of circular orbits for both the particles is equal and kinetic energy acquired by deutron is I Me V, then kinetic energy acquired by the proton particle will be . 

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  1. 1 MeV

  2. 2 MeV

  3. 0.5 MeV

  4. 4 MeV

Show answer
Correct Option: A
Explanation:

$R = \dfrac{{mv}}{{qB}} = \dfrac{{\sqrt {2mk} }}{{qB}}{K _p} = \dfrac{{{q^2}{B^2}R _p^2}}{{2mp}}$

$k = \dfrac{{{q^2}{B^2}{R^2}}}{{2m}}$
$\therefore \dfrac{{{K _\infty }}}{{{K _p}}} = {\left( {\dfrac{{{q _\infty }}}{{q{I _0}}}} \right)^2}\left( {\dfrac{{{m _p}}}{{{m _\infty }}}} \right){\left( {\dfrac{{{R _p}}}{{{R _\infty }}}} \right)^2}$
$ \Rightarrow {K _\infty } = {K _p}{\left( {\dfrac{{{q _\infty }}}{{{q _p}}}} \right)^2}\left( {\dfrac{{mp}}{{{m _\infty }}}} \right){\left( {\dfrac{{{R _\infty }}}{{{R _p}}}} \right)^2}$
${K _p} = 1MeV{\left( 2 \right)^2}{\left( {\dfrac{1}{4}} \right)^2}{\left( 1 \right)^2} = 1MeV$
Hence,
option $(A)$ is correct answer.

If K.E. body is increased by 100 % then % change in its momentum is:

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  1. 50%

  2. 41.4%

  3. 10%

  4. 20%

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Correct Option: A

A 200 gm mass has velocity of $(3\hat i+4\hat j)$m/s at certain instant. Find its kinetic energy. 

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  1. $2.5 J$

  2. $0.5 J$

  3. $0.8 J$

  4. $1.5 J$

Show answer
Correct Option: A
Explanation:

First we will calculate the Magnitude of velocity  so $v=\sqrt{3^2+4^2}=5\ m/s$

Now m=200 gm or 0.2 kg

So $KE=\dfrac{mv^2}{2}=\dfrac{0.2\times 5^2}{2}$

so $KE=2.5\ J$

A proton is kept at rest. A positively charged particle is released from rest at a distance $d$ in its field. Consider two experiments; one in which the charged particle is also a proton and in another, a positron. In the same time $t$, the work done on the two moving charged particles is:

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  1. same as the same force law is involved in the two experiments

  2. less for the case of a positron, as the positron moves away more rapidly and the force on it weakens

  3. more for the case of a positron, as the positron moves away a larger distance.

  4. same as the work done by charged particle on the stationary proton

Show answer
Correct Option: C
Explanation:
 The force between two protons is equal to the force between the proton and a position because their charges are same. As the mass of positron is much lesser than a proton, (1/1840 times) it moves away through much larger distance compared to proton. Change in their momentum will be same. So, a velocity of a lighter particle will be greater than that of a heavier particle. So, a positron is moved through a larger distance.
As $work done = force \times distance$. As forces are same in case of proton and positron but distance moved by positron is larger, hence, work done will be more.

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because

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  1. The two magnetic forces are equal and opposite, so they produce no net effect

  2. The magnetic forces do no work on each particle

  3. The magnetic forces do equal and opposite (but non-zero) work on each particle

  4. The magnetic forces are necessarily negligible

Show answer
Correct Option: B
Explanation:

As the magnetic forces due to motion of electron and proton act in a direction perpendicular to the direction of motion, no work is done by these forces. That is why one ignores the magnetic force of one particle on another.

A car starts from rest and moves on a surface in which the coefficient of friction between the road and the tyres increases linearly with distance (x). If the car moves with the maximum possible acceleration, the Kinetic energy (E) of the car will depend on x as:

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  1. $E\propto\dfrac{1}{x^2}$

  2. $E\propto\dfrac{1}{x}$

  3. $E\propto{x}$

  4. $E\propto{x^2}$

Show answer
Correct Option: D
Explanation:

Support car moves a distance dx at a distance x.

$\mu=kx$
$f _r=kx(mg)$
Work done by friction $=K.E(E)$
$E=f _r dx=mg kx dx$
$E \propto x^2$

Consider the following two statement 
A) Linear momentum of a system of particles is zero.
B) Kinetic energy of a system of particles is zero 

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  1. A does not imply B and B does not imply A

  2. A Implies B but B does not imply A

  3. A does not imply B but B implies A

  4. A implies B and B implies A

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Correct Option: A

The kinetic energy of an electron which is accelerated through a potential of $100$ volts is?

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  1. $1.602\times 10^{-17}$ joules

  2. $418.6$ calories

  3. $1.16\times 10^4$ eV

  4. $6.626\times 10^{-34}$ watt-second

Show answer
Correct Option: A
Explanation:

According to de Broglie equation,Wavelength associated with an electron through potential difference V is given as

$\lambda =\frac { 12.27 }{ \sqrt { V }  } A=\frac { 12.27 }{ \sqrt { 100 }  } A=\frac { 12.27 }{ 10 } A=1.227A$

When an object is made up of n number of particles we refer to it (object) as a system of Particles

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  1. True

  2. False

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Correct Option: A
Explanation:

According to definition of system of particles

"When a object is made up of more than 1 particle then we refer that object to be as a system of particles

Hydrogen fuel is used in:

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  1. liquid-propellant rockets

  2. portable fuel cell applications

  3. cars

  4. all of above

Show answer
Correct Option: D
Explanation:

Hydrogen fuel can provide motive power for liquid-propellant rockets, cars, boats and airplanes, portable fuel cell applications or stationary fuel cell applications, which can power an electric motor. The problems of using hydrogen fuel in cars arise from the fact that hydrogen is difficult to store in either a high pressure tank or a cryogenic tank.