Law of Conservation of Energy

Q. A point charge $q_1=9.1\mu \text{C}$ is held fixed at origin. A second point charge $q_2=-0.42\mu \text{C}$ and a mass $3.2\times {10}^{-4}\text{kg}$ is placed on the $\text{x-axis}$, $0.96\text{m}$ from the origin. The second point charge is released at rest. What is its speed when it is $0.24\text{m}$ from the origin?

1. $15{\text{ms}}^{-1}$
2. $10{\text{ms}}^{-1}$
3. $42{\text{ms}}^{-1}$
4. $26{\text{ms}}^{-1}$

Q.

Total Energy of the universe is constant?

1. Yes, of course

2. No, it’s conserved but not constant.
3. Only mechanical energy is conserved.
4. Can't say

Q. A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is $4R$. The angle of projection, $\theta$ is then given by :

1. $\theta ={\cos }^{-1}{\left(\frac{{\pi }^{2}R}{g{T}^2}\right)}^{1/2}$
2. $\theta ={\sin }^{-1}{\left(\frac{{\pi }^{2}R}{g{T}^2}\right)}^{1/2}$
3. $\theta ={\sin }^{-1}{\left(\frac{2g{T}^2}{{\pi }^{2}R}\right)}^{1/2}$
4. $\theta ={\cos }^{-1}{\left(\frac{g{T}^2}{{\pi }^{2}R}\right)}^{1/2}$

Q. A charge $q={10}^{-6}C$ of mass $2g$ is free to move when released at a distance ${}^{\prime }{a}^{\prime }$ from the fixed charge $Q$.
Calculate its speed, when it moves to a distance $b$
[Assume $a=1\text{m}$, $b=10\text{m},Q={10}^{-3}\text{C}]$

1. $90\text{m/s}$
2. $9\text{m/s}$.
3. $900\text{m/s}$.
4. None of these

Q. From a planet of mass $16M$ and radius $4R$, we wish to send an object to its moon of mass $M$ and radius $R$. Distance between centres of planet and moon is $10R$. Minimum speed at which object should be projected from the surface of planet so that it reaches moon is (Assume that the planet and the moon are at rest)

1. $\sqrt{\frac{10GM}{3R}}$
2. $\sqrt{\frac{8GM}{R}}$
3. $\sqrt{\frac{7GM}{3R}}$
4. $\sqrt{\frac{9GM}{2R}}$

Q. Four masses of $1\text{kg}$ each are placed to form a square as shown. What will be the magnitude of work required to double the length of the square keeping the masses at the corners?

1. $W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$
   
2. $W=G\left(\frac{2\sqrt{2}-1}{3\sqrt{2}}\right)$
3. $W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$
4. $W=G\left(\frac{2\sqrt{2}-1}{\sqrt{2}}\right)$

Q. Tony Stark wants to build an engine to propel his Iron Man suit; he wants to achieve an efficiency of 1.5 to make the suit lighter and faster! Which of the following laws of physics would he be violating?

1. 1${}^{st}$ law of Thermodynamics
2. 2${}^{nd}$ law of Thermodynamics
3. Both (a) and (b)
4. Neither (a) and (b)

Q. How much energy is needed to move a body of ${10}^{3}kg$ mass from Earth's surface to a height of $2R_E$?$(R_E=radiusofEarth=6400km)$

1. $42\times {10}^{9}J$
2. $36\times {10}^{9}J$
3. $64\times {10}^{3}J$
4. $84\times {10}^{3}J$

Q.

Under a constant Electric field of 5 N/C, a positive charge moves such that its Kinetic energy is increased by 10 J. Assuming no other force acting, the work done by the field is?

1. 10 J

2. -10 J

3. 0 J

4. None of these ​​

Q. A charge $q={10}^{-6}C$ of mass $2g$ is free to move when released at a distance ${}^{\prime }{a}^{\prime }$ from the fixed charge $Q$.
Calculate its speed, when it moves to a distance $b$
[Assume $a=1\text{m}$, $b=10\text{m},Q={10}^{-3}\text{C}]$

1. $90\text{m/s}$
2. $9\text{m/s}$.
3. $900\text{m/s}$.
4. None of these