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If the potential energy of a gas molecule is

U= M/r^{​​​​​​6} - N/r^{​​​​​​12}

M&N being positive constant, then the potential energy at equilibrium must be

a: zero. b: M²/4N. c:NM^{​​​​​2}/4. d:MN​​​​​​​​²/4

When $100\text{V}$ $DC$ is applied across a coil, a current of $1\text{A}$ flows through it. When $100\text{V}$ $AC$ of $50\text{Hz}$ is applied to the same coil, only $0.5\text{A}$ current flows. Calculate the inductance of the coil.

An electron having de-Broglie wavelength $\lambda$ is incident on a target in a $\text{X}-\text{ray}$ tube. Cut-off wavelength of emitted $\text{X- ray}$ is :

(Symbols have their usual meaning)

At what temperature does the rms speed of oxygen molecules equal the escape velocity of - (i) Earth, (ii) the Moon? Assume gravitational acceleration at the moon is 0.6g.

For the shown $L-C$ circuit, the capacitor is first charged to $200\mu \text{C}$ and then connected with inductor. When instantaneous current is equal to one- half of its maximum value, then the value of instantaneous charge on capacitor is

A charged particle is fired at an angle $\theta$ to a uniform magnetic directed along the $x$-axis. During its motion along a helical path, if the pitch of the helical path is equal to the maximum distance of the particle from the $x$-axis.

A point $C=\frac{5\overrightarrow{a}+4\overrightarrow{b}-5\overrightarrow{c}}{3}$ divides the line joining $A=\overrightarrow{a}-2\overrightarrow{b}+3\overrightarrow{c}$ and $B$ in the ratio $2:1,$ then $\overrightarrow{AB}$ is

Three identical circular plates of radius $R$ each are placed on a horizontal surface touching one another as shown in the figure. The y coordinate of the center of mass of the system is [Consider $\text{A}$ to be at the origin]

A charged particle is accelerated through a potential difference of 12 KV and aquires a speed of 1 ×10^6 m/s . It is then injected perpendicularly into a magnetic field of strength 0.2T . Find the radius of the circle described by it.

What are the merits of Dalton’s atomic theory?

When a coil of area $0.2{\text{cm}}^2$, having $30$ turns and whose plane is normal to the magnetic field is drawn out of the magnetic field, a charge of $1.5\times {10}^{-4}\text{C}$ flows in the circuit. If its resistance is $40\Omega$, then the magnetic flux density will be

In the given series LCR circuit, the reading of the hot wire voltmeter $\left(V\right)$ across resistor will be -

The particle $P$ shown in figure has a mass of $10\text{mg}$ and a charge of $-0.01\mu \text{C}$. Each plate has a surface area $100{\text{cm}}^2$ on one side. What potential differences $V$ should be applied to the combination to hold $P$ in equilibrium ?

A particle is performing a linear simple harmonic motion. If the acceleration and the corresponding velocity of the particle are a and v respectively, which of the following graphs is correct?

A particle of charge q and mass m moving with velocity v along the x - axis enters the region x>0 with uniform magnetic field B along positive z direction. The particle will penetrate in this region along x - axis up to a distance d equal to

For any real $t,x=\frac{e^x+e^{-x}}{2},y=\frac{e^x-e^{-x}}{2}$ is a point on the hyperbola $x^2-y^2=1$. The area bounded by the hyperbola and the lines joining its centre to the points corresponding to $t_1$ and $-t_1$ is

Two particles having masses $3\text{kg}$ and $6\text{kg}$ are situated in a plane perpendicular to line $AB$ at a perpendicular distance of $2\text{m}$ and $4\text{m}$ respectively as shown in figure. Find the moment of inertia about an axis $A^{\prime }{B}^{\prime }$ parallel to $AB$.

If two charged particles each of charge $q$ and mass $m$ are connected to the ends of a rigid massless rod of length $l$ and is rotated about an axis passing through the center and perpendicular to length. Then the ratio of magnetic moment to angular momentum is-

A wave going in a solid

Two tuning forks of frequency 250Hz and 256Hz produce beats. If a maximum intensity is observed at t = 0. At what time instant(s), the minimum intensity is observed at the same place?

A body $A$ starts from rest with an acceleration $a_1$ . After $3$ seconds, another body $B$ starts from rest with an acceleration $a_2$ . If they travel equal distances in the $6^{\text{th}}\text{second}$ after the start of $A$, then the ratio $a_1:a_2$ is equal to

A uniform chain has a mass M and length L. It is placed on a frictionless table with length $L_0$ hanging over the edge. The chain begins to slide down. Then, the speed v with which the end slides down from the edge is given by

A particle located in a one - dimentional potential field has its potential energy functions as U(x) = $\frac{a}{x^4}-\frac{b}{x^2}$, where a and b are positive constants. The positionof equilibrium x corresponds to

If a man travels 10 $km$ towards north, then he turns towards east and travels 5 $km$ and again he turns toward south and travels 3 $km$, then what is the coordinate of man with respect to its initial position.(Assume $X-axis$ is towards East, $Y-axis$ is towards North)

A man in a balloon rising vertically with an acceleration of $4.9{\text{m/s}}^2$ releases a ball $2\text{s}$ after the balloon has left the ground. The greatest height above the ground, reached by ball is $(g=9.8{\text{m/s}}^2)$

For the myopic eye, the defect is cured by

[CPMT 1990; KCET (Engg.) 2000]

An object is displaced from position vector ${\overrightarrow{r}}_1=(2\hat{i}+3\hat{j})\text{m}$ to ${\overrightarrow{r}}_2=(4\hat{i}+6\hat{j})\text{m}$ under the action of a force $\overrightarrow{F}=(3x^2\hat{i}+2y\hat{j})N$. Find the work done by this force.

The
plates of a parallel plate capacitor have an area of 90 cm²
each and are separated by 2.5 mm. The capacitor is charged by
connecting it to a 400 V supply.

(a) How
much electrostatic energy is stored by the capacitor?

(b) View
this energy as stored in the electrostatic field between the plates,
and obtain the energy per unit volume u.
Hence arrive at a relation between u
and the magnitude of electric field
E between
the plates.

Magnitude of surface charge density on each plate of a parallel plate capacitor is $88.5\mu {\text{C/m}}^2$. What is the magnitude of the electric field in the region between the plates?

(Take ${ϵ}_o=8.85\times {10}^{-12}{\text{C}}^2{\text{/N m}}^2$)

Consider a long wire carrying a time varying current $i=kt(k>0)$. A circular loop of radius $a$ and resistance $R$ is placed with its center at a distance $d$ from the wire $(a<<d)$. The induced current in the loop is

A particle moves with a velocity, $\overrightarrow{v}=(5\hat{i}-3\hat{j}+6\hat{k})\text{m/s}$ at an instant, under the influence of a constant force, $\overrightarrow{F}=(10\hat{i}+10\hat{j}+20\hat{k})\text{N}$. The instantaneous power applied to the particle is

Air is streaming past a horizontal aeroplane wing such that its speed is $120\text{m/s}$ over the upper surface and $90\text{m/s}$ at the lower surface. If the density of air is $1.3{\text{kg/m}}^3$ and wing is $10\text{m}$ long and has an average width $2\text{m}$, calculate the gross lift of the wing.

A particle starting from rest travels a distance x in first 2 seconds and a distance y in next two seconds, then

Which celestial bodies form the solar system?

Going by the pattern of replacing words. If I do draw the a-t graph, the area under graph(the integral) will give the