Law of Conservation of Energy

Q. A charge $Q$ is placed at each of the two opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the resultant force on each charge $q$ is zero, then

1. $q=\sqrt{2}Q$
2. $q=-\sqrt{2}Q$
3. $q=2\sqrt{2}Q$
4. $q=-2\sqrt{2}Q$

Q. A point charge $50\mu \text{C}$ is located in the $\text{XY-}$plane at the point of position vector ${\overrightarrow{r}}_0=2\hat{i}+3\hat{j}$. Find the electric field ($\text{V/m}$) due to this point charge at the point of position vector $\overrightarrow{r}=8\hat{i}-5\hat{j}$

Q.

Two stones are thrown vertically upwards simultaneously with their initial velocities $u_1$ and $u_2$ respectively. Calculate the ratio of heights reached by them.

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

Q.

An object is dropped from a cliff falls with a constant acceleration of $10m/s^2$. Find its speed 2s after it was dropped.

Q. An alpha particle is accelerated through a potential difference of ${10}^6\text{volt}$. Its kinetic energy will be

1. $1\text{MeV}$
2. $2\text{MeV}$
3. $4\text{MeV}$
4. $8\text{MeV}$

Q. Find the distance of the point from $A,$ where the net electric field will be zero for the given configuration.

1. $\frac{1}{3}\text{m}$ towards right
2. $\frac{2}{3}\text{m}$ towards right
3. $\frac{4}{3}\text{m}$ towards right
4. $\frac{5}{3}\text{m}$ towards right

Q. If an electron moves in the direction of electric field, then

1. Both kinetic energy and potential energy will increase.
2. Its kinetic energy will decreases and potential energy will increase.
3. Both kinetic energy and potential energy will decrease.
4. Kinetic energy will increase and potential energy will decrease.

Q. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of the line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to

1. go straight
2. turn right
3. turn left
4. turn left and right alternately

Q. The escape velocity from a planet is ${\text{v}}_e$. A particle starts from rest at a large distance from the planet, reaches the planet only under gravitational attraction, and passes through the smooth tunnel through its center, its speed at the center of the planet will be :

1. $\sqrt{1.5}{\text{v}}_e$
2. $\frac{{\text{v}}_e}{\sqrt{2}}$
3. ${\text{v}}_e$
4. Zero

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.

Total Energy of the universe is constant?

1. Yes, of course

2. No, it’s conserved but not constant.
3. \N
4. \N

Q. The lines of force of the electric field of a positive charge $(+q)$ and a negative charge $(-q)$ are shown in figure (a) and (b) below. Then:-

(a) The work done in moving a small positive charge (+$q_0$) from Q to P will be positive
(b) The work done in moving a small negative charge (−$q_0$) from B to A will be positive
(c) In going from Q to P, the kinetic energy of a small negative charge (−$q_0$) increases
(d) In going from B to A, the kinetic energy of a small negative charge (−$q_0$) decreases

1. Only a
2. a and b
3. a, c, d
4. a, b, c, d

Q.

The two wires shown in figure are made of the same

material which has a breaking stress of $8{\times }^{8}N{M}^{-2}$. The area of cross section of the upper wire is $0.006c{m}^2$ and that of the lower wire is $0.003c{m}^2$. The mass $m_1=10kg,m_2=20kg$ and the hanger is light. (a) Find the maximum load that can be put on the hanger without breaking a wire. Which wire will break first if the load is increaed ? (b) Repeat the above part if $m_1=10kg$ and $m_2=36kg.$

Q. the K.E. of a satellite is 2mj what is the total energy of the satellite?

Q. Two springs are connected to a block of mass $M$ placed on a frictionless surface as shown below. If both the springs have a spring constant $k$, the frequency of oscillation of block is

1. $\frac{1}{2\pi }\sqrt{\frac{k}{M}}$
2. $\frac{1}{2\pi }\sqrt{\frac{k}{2M}}$
3. $\frac{1}{2\pi }\sqrt{\frac{2k}{M}}$
4. $\frac{1}{2\pi }\sqrt{\frac{M}{k}}$

Q. Proton and electron are projected perpendicular to the same uniform electric field from the same point in same direction then which will have more magnitude of deflection for the same displacement perpendicular to electric field ? 1.They have same initial kinetic energy 2.They have same initial velocity.

Q. Six identical charges \(+q\)are placed at the corners of a regular hexagon shown in the figure. The charge \(Q\), that should be placed at the centre of hexagon so that the net force on the charge placed at any corner is zero

B 

Q. A load of $10\text{kN}$ is supported from a pulley which in turn is supported by a rope of cross-sectional area ${10}^3{\text{mm}}^2$ and modulus of elasticity ${10}^3{\text{N/mm}}^2$ as shown in the figure. Neglecting friction at the pulley, downward deflection of the load $\left(\text{in mm}\right)$ is

1. $3.75$
2. $4.25$
3. $2.75$
4. $4.00$

Q. A proton has mass 1.6×10^{-27} kg and charge 1.6×10^{-19 c} if proton is accelerated through a potential difference of million volts, then the kinetic energy i

Q. A ball of small size is released from height $R_E$, find the speed of ball when it reaches the surface of earth. Assume $R_E$ is the radius of earth and $g$ is acceleration due to gravity on earth's surface.

1. None
2. $\sqrt{2g{R}_E}$
3. $\sqrt{g{R}_E}$
4. $\sqrt{\frac{g{R}_E}{2}}$

Q. The charge and mass of a particle are $2$ times and $4000$ times the charge and mass of an electron respectively, and is at rest. If this particle is accelerated through a potential difference of $5\text{V}$ then its final kinetic energy will be-

1. $5\text{eV}$
2. $10\text{eV}$
3. $15\text{eV}$
4. $20\text{eV}$

Q.

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = 6.0 ×10²⁴ kg; radius of the earth = 6.4 ×10⁶ m; G = 6.67 × 10^–11 N m² kg^–2.

Q. A charge of mass $50\text{mg}$ and carrying $5\times {10}^{-9}\text{C}$ is approaching a fixed of ${10}^{-8}\text{C}$ with a velocity of $0.5{\text{ms}}^{-1}$. The distance of closest approach of the charge is

1. $1.2\text{cm}$
2. $4.2\text{cm}$
3. $7.2\text{cm}$
4. $8.6\text{cm}$

Q. A particle of mass $1\text{kg}$ and charge $-2\mu \text{C}$(initially at a very large distance) is projected with initial velocity $200\text{m/s}$ towards a positive charged particle of charge $2\mu \text{C}$ which is fixed. The distance of $1\text{kg}$ particle from heavy particle when speed of $1\text{kg}$ particle is equal to twice of initial value is $\frac{x}{{10}^7}\text{m}$. Find the value of ‘$x$’.

Q. Would it be right to ask someone to prove the law of conservation of energy?

Q. Two charges of charge $+1\text{C}$ are connected by a spring of spring constant $100\text{N/m}$ and length $1\text{m}$. A small displacement in charge $2$ results into oscillation of the system. Calculate the time period of oscillation.
(mass of charge is $1\text{gm})$

1. $1.5\mu \text{s}$
2. $2.2\mu \text{s}$
3. $3.1\mu \text{s}$
4. $1.0\mu \text{s}$

Q. The energy stored in the condenser is

1. QV
2. 0.5QV
3. 0.5C
4. 0.5 Q/V

Q. A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire becomes $1.1L$ when a mass $M$ is suspended from its free end. The Young's modulus of wire is given by

1. $\frac{Mg}{A}$
2. $\frac{10Mg}{A}$
3. $\frac{40Mg}{A}$
4. $\frac{4Mg}{A}$

Q. Two charged particles having charge $2.0\times {10}^{-8}C$ each are joined by an insulating string of length $1m$ and the system is kept on a smooth horizontal table. Find the tension in the string.