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Figure (17-E5) shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let $B{P}_0-A{P}_0=\frac{\lambda }{3}$ and D >> \lambda (a) show that in this case $d=\sqrt{\frac{2\lambda d}{3}}.$
(b) Show that the intensity at $P_0$ is three times the intensity due to any of the three slits individually.

Find the time period of the oscillation of mass m in figures 12-E4 a,b,c. What is the equivalent spring constant of the pair of springs in each case ?

how to convert 1N force into F.P.S system ?

From the top of a tower of height 490 m, a shell is fired horizontally with a velocity 100 m/s. At what distance from the bottom of the tower, the shell will hit the ground ? (Give the answer in m)

In the case of deducting relation among the physical quantities,how can I find the value of the constant?

Two people $A$ and $B$ of mass $m$ and $2m$ are standing at the two ends of the wooden plank of mass $8m$. Both people start walking towards each other. Find the ratio of the velocities of $A$ and $B$ so that the plank will remain at rest.

A particle moves in a circle of radius $1\text{m}$ with a uniform speed, it completes one revolution in $2\pi \text{seconds}$, the acceleration of the particle is

A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.
(Hint: The moment of inertia of the door about the vertical axis at one end is $M{L}^2/3$.)

The capacitance of the capacitor of plate areas $A_1$ and $A_1$at a distance d, as

shown in the figure, is:

If I drop ball A vertically and throw ball B horizontally both from a height h above the ground then which will hit the ground first

A rectangular plate of sides a and b is suspended from a ceiling by two parallel strings of length L each (figure). The separation between the strings is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute simply harmonic motion. Find the time period.

A block of mass of $10kg$ is in contact with the inner wall of a hollow cylindrical drum of radius $1m.$ The coefficient of friction between the block and the inner wall of the cylinder is $0.1.$ The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be $\left(g=10m/s^2\right)$

Gas Bubbles from an explosion underwater oscil lates with a period to prproportional to P^{​​​​​​a} rho^{​​​​b} E^{​​​​​​c} where P is the state pressure, rho is the density of water and E is the total energy of the explosion find the values of a b and c

the most incomprehensible thing about world is that it is most comprehensible meaning of this sentence by einstein

Each side of cube is L then magnitude of magnetic dipole moment of loop oabcdeo carrying current i as shown in figure is.

A man standing on a road has to hold his umbrella at ${30}^{\circ }$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10{\text{kmh}}^{-1}$ . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is

Mass of block $A$ is $1\text{kg}$ and that of block $B$ is $2\text{kg}$. If a horizontal force $F=10\text{N}$ is applied on the pulley, find the acceleration of block $A$ and block $B$ respectively. All surfaces are frictionless.

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
(a) How much work does she do against the gravitational force?
(b) Fat supplies $3.8\times {10}^{7}J$ of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

Figure (38-E2) shows a conducting square loop placed parallel to the pole-faces of a ring magnet. The pole -faces have an area of $1c{m}^2$ each and the field between the poles is 0.10 T. The wires making the loop are all outside the magnetic field. If the magnet is removed in 1.0 s, what is the average emf induced in the loop?

In vertical circular motion, the ratio of kinetic energy of a particle at highest point to lowest point is (Particle is just completing vertical circular motion)

In the block diagram of a simple modulator for obtaining an AM signal, shown in the figure, identify the boxes A and B. Write their functions

A particle is located at $(3\text{m},4\text{m})$ and moving with $\overrightarrow{v}=(4\hat{i}-3\hat{j})\text{m/s}$. Find the magnitude of angular velocity about origin at this instant.

A particle moves in a circle of radius $1.0cm$ at a speed given be $v=2.0t$ where $v$ is in $cm/s$ and $t$ is in seconds. Find the magnitude of net acceleration at $t=1s$.

A Block is released from rest at the top of an inclined plane which later curves into a circular track of radius r as shown. Find the minimum height h from where it should be released so that it is able to complete the circle.

In an L–R circuit $L=\frac{0.4H}{\pi }$ and R = 30 $\Omega$ If the circuit has an alternating emf of 220 volt and its frequency 50 cycles per sec, the impendence and current in the circuit respectively will be

An infinite number of electric charges each equal to $5\times {10}^{-9}C$ are placed along X – axis at x = 1 cm, x = 3 cm, x = 9 cm, x =27 cm ………. And so on. If the consecutive charges have opposite sign,
Then the electric field in $\frac{N}{C}$ at x = 0 is $(\frac{1}{4\pi {ϵ}_0}=9\times {10}^{9}N{m}^2/C^2)$

Two particles A and B are moving with uniform velocities as shown in the figure given below at $t=0$. Find out the shortest distance between the two particles

A thin hollow sphere of mass $m$ is completely filled with water of mass $m$. Now it is kept in a refrigerator and cooled to below $0^{\circ }\text{C}$. It is taken out and made to roll without slipping on a horizontal surface with a velocity $u$. The kinetic energy of the system is (Assume no heat is gained by the sphere)

The coefficient of friction between wedge A and block B is $\mu$. The wedge A accelerates at rate $am/s^2$ such that block B will remain at rest with respect to the wedge. Then for what value of $\theta$, we get $a=g\left[\frac{1+\mu }{1-\mu }\right]$?

A person speaking normally produces a sound Intensity of 40 dB at a distance of 1m. If the threshold Intensity for reasonable audibility is 20 dB, the maximum distance at which he can be heard clearly is:

A particle of charge q and mass m initially at rest, starts moving from the origin under the action of an electric field $\overrightarrow{E}=E_0\hat{i}$ and a magnetic field $\overrightarrow{B}=B_0\hat{i}$ with velocity $\overline{v}=v_0\hat{j}$ . The speed of the particle will become $2v_0$ after a time

A box when dropped from a certain height reaches the ground with a speed $v$. When it skids from rest from the same height down a rough inclined plane inclined at an angle ${45}^{\circ }$ to the horizontal, it reaches the ground with a speed $\frac{v}{3}$. The coefficient of sliding friction between the box and the plane is (acceleration due to gravity is $10m{s}^{-2}$ )

The principle used in the transmission of signals through an optical fibre is

A car of mass m moving along a circular track of radius r with a speed v which varies with time t as v=kt, k being a constant. Then,

A potentiometer wire of length 200 cm has a resistance of $20\Omega$ . It is connected in series with a resistance of $10\Omega$ and an accumulator of emf 6 V having negligible internal resistance. A source of 2.4 V is balanced against a length L of the potentiometer wire. The value of L is

The energy of an electron in excited hydrogen atom is $-3.4eV$. Then according to Bohr's theory the angular momentum of the electron in $Js$ is

Wavelength of two notes is air $\frac{80}{195}$ m and $\frac{80}{193}$ m. Each note produces 5 beats per second with a third note of a fixed frequency. The speed of sound in air is:

A billiard ball is hit by a cue at height $h$ above the centre. It acquires a linear velocity $V_0$. Mass of the ball is $m$ and radius is $r$. The angular velocity ${\omega }_0$ acquired by the ball is

An ideal spring having force constant k is suspended from the rigid support and a block of mass M is attached to
its lower end. The mass is released from the natural length of the spring. Then the maximum extension in the spring is

A cell of e.m.f. E is connected with an external resistance R , then p.d. across cell is V . The internal resistance of cell will be