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In a single slit diffraction experiment, the slit width is made double that of the original width. Why does the area of diffraction become 1/4?

For the given figure List - I gives acceleration of blocks of masses $m_1,m_2,m_3\&m_4$ and List - II gives their magnitudes. Here $m_1=m_2=2m$ and $m_3=m_4=m$

$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{(I)}{a}_1& \text{(P)}2g\\ \text{(II)}{a}_2& \text{(Q)}g\\ \text{(III)}{a}_3& \text{(R)}\frac{g}{2}\\ \text{(IV)}{a}_4& \text{(S)}\frac{g}{4}\\ & \text{(T)}0\\ & \text{(U)}\text{None}\end{array}$
Just after cutting string connecting $m_1$ and $m_2$ correct match for accelerations of blocks is

Minimum value of $F$ for which the cube begins to tip about an edge is equal to $\frac{2mg}{M}$. Then, $M$ is -

Natural length of a massless spring (of spring constant $k$) is $x$. It is slowly stretched by applying an external force. What is the work done in slowly increasing its extension from $3x$ to $4x$?

When a metal plate is exposed to a monochromatic beam of light of wavelength 400 nm, a negative potential of 1.1 V is needed to stop the photo current. Find the threshold wavelength for the metal.

The energy of a photon is E=hv and the momentum of photon $p=\frac{h}{\lambda }$, then the velocity of photon will be

The value of g at a place decreases by 2%. The barometric height of mercury

A monoatomic gas molecule has

How ac current is obtained

One end of a cylindrical glass rod shown in figure ends in a hemispherical surface of radius R = 20 mm.
-Let the same rod be immersed in water of index 1.33, the other quantities having the same values as before. Find the image distance.

A body is thrown with a velocity of 9.8 m/s making an angle of ${30}^{\circ }$ with the horizontal. It will hit the ground after a time

Two particles are executing SHM of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their amplitude. The phase difference between them is

Figure shows a cylindrical tube of volume V with adiabatic walls containing an ideal gas. The internal energy of this ideal gas is given by $1.5nRT$. The tube is divided into two equal parts by a fixed diathermic wall. Initially, the pressure and the temperature are $p_1$, $T_1$ on the left and $p_2$, $T_2$ on the right. The system is left for sufficient time so that the temperature becomes equal on the two sides.

(a) How much work has been done by the gas on the left part ?

(b) Find the final pressures on the two sides.

(c) Find the final equilibrium temperature.

(d) How much heat has flown from the gas on the right to the gas on the left ?

In a series circuit R = 300 $\Omega$ , L = 0.9 H, C = 2.0 $\mu$F and $\omega$ = 1000 rad/sec. The impendence of the circuit is

The tangent drawn from a point P outside the circle with centre O is shown. Find the value of `x'.

Two infinitely long parallel wires having linear charge densities ${\lambda }_1$ and ${\lambda }_2$ respectively are placed at a distance of R metres. The force per unit length on either wire will be $(K=\frac{1}{4\pi {ϵ}_0})$

In Young's double -slit experiment, the intensity of light at a point on the screen, where the path difference is $\lambda$ , is I. The intensity of light at a point where the path difference becomes $\frac{\lambda }{3}$ is

A demo CD, 8 cm in diameter, spins 200 rev/min. Determine its linear velocity in cm/s for a point 3 cm from the center.

A ray of light through B(3, 2) is reflected at the point $A(0,\beta )$ on the y-axis and passes through C(4, 3). Then $\beta$ =

A person standing on the top of a cliff 171 ft high has to throw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend at the friend wuth a speed of 15.0 ft/s, how short will the packet fall ?

In a fission reaction
${}_{92}^{238}U\to {}^{117}X{+}^{117}Y+n+n$
the binding energy per nucleon of X and Y is 8.5 MeV whereas that of ${}^{236}U$ is 7.6 MeV. The total energy liberated will be about

What is the equivalent capacitance between points A and B?

Three particles each of mass m, are placed at the corners of an equilateral triangle of side a, as shown in the figure. The position vector of the centre of mass is

Angle between the planes $x+y+2z=6$ and $2x-y+z=9$ is,

A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

If a function is given as $y=ln\left(sinx\right)$, then the first derivative of $y$ w.r.t. $x$ will be

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth $(\text{mass}=6\times {10}^{24}\text{kg})$ have to be compressed to be a black hole?

An electric current flows along conductor AB as shown in figure.

$\overrightarrow{E}$ in conductor AB varies as

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

In previous question after what time the passenger catches bus ?

A small trolley of mass 2 kg resting on a horizontal frictionless turntable is connected by a light spring to the centre of the table. The relaxed length of the spring is 35 cm. when the turntable is rotated an angular frequency of 10 rad $s^{-1}$ the length of the spring becomes 40 cm. what is the force constant of the spring?

What is the maximum speed with which a vehicle can negotiate a convex bridge of radius $10\text{m}$ without leaving the surface of the road.
(Take $g=10{\text{m/s}}^2$)

Which of the following graphs cannot possibly represent one dimensional motion of a particle?

A particle moves in x-y plane according to equation $\overrightarrow{S}=(2\hat{i}+\hat{j})cos\omega t$ The motion of particle is

When ${}_{92}{U}^{237}$ nucleus is converted into ${}_{83}B{i}^{209},x$ and $y$ are the number of $\alpha$ and $\beta$ particles emitted respectively then the value of $x$ and $y$, are respectively

A long straight wire carries a current along the x-axis. Consider the points A(0, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(1, 1, 1). Which of the following pairs of points will have magnetic fields of the same magnitude?

Photons with energy $5\text{eV}$ are incident on a cathode C, on a photoelectric cell. The maximum energy of the emitted photoelectrons is $2\text{eV}$. When photons of energy $6\text{eV}$ are incident on C, no photoelectrons will reach the anode A if the stopping potential of A relative to C is

If $\frac{\sin \theta }{x}=\frac{\cos \theta }{y}$, then $\sin \theta -\cos \theta$ is

Time period T of a simple pendulum may depend upon mass of the bob m; length of simple pendulum ‘$\ell$ ’ and ‘g’ the acceleration due to gravity as $T\alpha m^a{l}^b{g}^c$. Then the value of a, b and c are:

A particle of mass m moving with a speed v hits elastically another stationary particle of mass 2 m on a smooth horizontal circular tube of radius r. The time in which the next collision will take place is equal to