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The radius of first Bohr's orbit of hydrogen atom is $0.53\dot{A}$. Then the radius of first Bohr's orbit of Mesonic atom [negative meson has mass $207$ times that of electron but same charge] is :

A capacitor of capacitance $4\mu \text{F}$ is charged upto $80\text{V}$ and another capacitor of capacitance $6\mu \text{F}$ is changed upto $30\text{V}$. When they are connected together the energy lost by the $4\mu \text{F}$ capacitor is

Two block $A$ and $B$ of mass $10\text{kg}$ and $20\text{kg}$ respectively, are arranged as shown in figure on a smooth horizontal surface. A constant force $F=60\text{N}$ acts on block $A$. Find the minimum coefficient of static friction (${\mu }_{\text{min}}$) so that both the block moves together without slipping? Take $g=10{\text{m/s}}^2$.

A body is thrown vertically upwards with an initial velocity u. It passes a point at a height h above the ground at time $t_1$ while going up and at time $t_2$ while falling down. Then the relation between u, $t_1$ and $t_2$ is

The linear density of a vibrating string is ${10}^{-4}kg/m$. A transverse wave is propagating on the string, which is described by the equation y = 0.02 sin (x + 30 t), where x and y are in meters and time t in seconds. Then tension in the string is

Which is valid when Fresnal distance is equal to D ( D =distance between the slit and screen]

Diffraction or ray optics

I know that diffraction is valid when it is much less than D ....

Greater than D then ray optics is valid

What if they are equal???

Pls ans in detail ☺

The minimum wavelength of X-rays emitted from an X-ray tube operating at a voltage of ${10}^{4}V$ is roughly equal to

The velocity of the centre of mass of a system changes form $\overrightarrow{V_1}=8\hat{i}\text{m/s}$ to $\overrightarrow{V_2}=6\hat{j}\text{m/s}$ during time interval $△t=3\text{s}.$ If the mass of the system is $m=6\text{kg}$, the constant force acting on the system is

The string shown in the figure is passing over a small smooth pulley rigidly attached to trolley A. If the speed of the trolley is constant and equal to $v_A$, speed and acceleration of block B at the instant is $v_B$ and $a_B$ respectively, which of the following option(s) is/are correct?

If pressure P, velocity V and time T are taken as fundamental physical quantities, then the dimensional formula for force is

An alternating voltage $E\text{(in volt)}=300\sqrt{2}\sin \left(100t\right)$ is connected to a $2\mu \text{F}$ capacitor through an AC ammeter. The reading of the ammeter would be

The two slits in Young's interference experiment have widths in the ratio n:1. The ratio of the intensities of the maxima and minima in the interference pattern is

Estimate the speed of vertically falling raindrops from the following data. Radius of the drops = 0.02 cm, viscosity of air = $1.8\times {10}^{-4}$ poise, g = $9.9\times 10m{s}^{-2}$ and density of water = $1000kg{m}^{-3}$

A dual slope A/D converter has resolution of 12-bits. If the clock rate is $100KHz,$ what is the maximum rate at which samples can be converted?

An infinite ladder network of resistance is constructed with a $1\Omega$ and $2\Omega$ resistance as shown in figure. What is the value of effective resistance between $\text{A}$ & $\text{B}$?

The peak power consumed by a resistive coil when connected to an AC source is 80 W. Find the enrgy consumed by the coil in 100 seconds which many times larger than the time period of the source.

If $x=at+b{t}^2$, where $x$ is the distance travelled by the body in kilometers while $t$ is the time in seconds, then the unit of $b$ is

If the ionisation energy for $H$ atom is $13.6eV$, then calculate the energy in eV when the atom is excited from the ground state to the first excited state?

A charged particle having mass $\left(m\right)$ and charge $\left(q\right)$ is projected from the origin with velocity $v=vo\hat{i}$ in a uniform magnetic field,$B=\frac{B_0}{2}\hat{i}+\frac{\sqrt{3}}{2}{B}_0\hat{j}$, where $B_0$ is a constant. The $z$-component of velocity is $\frac{\sqrt{3}}{2}{v}_0$ after time $t$. Find $t$.

When a resistor of $11\Omega$ is connected in series with an electric cell, the current flowing in it is $0.5\text{A}$. Instead, when a resistor of $5\Omega$ is connected to the same electric cell in series, the current increases by $0.4\text{A}$. The internal resistance of the cell is

Let the
vectors
given
as
.
Then show that

In Young's double slit experiment, two slits of equal intensities produce interference pattern forming central maxima at point $O$. A transparent film $(\mu =1.5)$ is placed in front of one of the slits. Now the intensity of light at point $O$ is $75\%$ of the intensity of a bright fringe. The wavelength of light used is $6000\mathring{\text{A}}$. The thickness of the film cannot be,

A light ray goes from a medium of refractive index$\sqrt{2}$ to a medium of refractive index 1. The minimum angle of incidence for TIR to happen is .

Two
inclined frictionless tracks, one gradual and the other steep meet at
A from where two stones are allowed to slide down from rest, one on
each track (Fig. 6.16). Will the stones reach the bottom at the same
time? Will they reach there with the same speed? Explain. Given θ₁
= 30°,
θ₂
= 60°,
and h =
10 m, what are the speeds and times taken by the two stones?

What is lens makers formula?

The fraction of a radioactive sample will decay during half of its half-life period is

The figure shows a square frame of wire placed coplanarly with a long straight wire. The wire carries a current given by $i=i_0\sin \omega t$. Find the expression for mutual inductance between the straight wire and the square loop.

An ac source of angular frequency $\omega$ is fed across a resistor r and a capacitor C in series. The current registered is I. If now the frequency of source is changed to $\frac{\omega }{4}$ (but maintaining the same voltage), the current in then circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$

Show that the magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis if the line joining the point with the centre of the dipole makes an an of tan ${}^{-1}\left(\sqrt{2}\right)$with the magnetic axis.

A shell of mass $1\text{kg}$ is projected with velocity $20\text{m/s}$ at an angle ${60}^{\circ }$ with horizontal. It collides inelastically with a ball of mass $1\text{kg}$ which is suspended through a thread of length $1\text{m}$. The other end of the thread is attached to the ceiling of a trolley of mass $\frac{4}{3}\text{kg}$ as shown in figure. Initially the trolley is stationary and it is free to move along horizontal rails without any friction. What is the maximum deflection of the thread with vertical? String does not slack. Take $g=10{\text{m/s}}^2$.