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The graph between 1/$\lambda$ and stopping potential (V) of three metals having work functions ${\Phi }_1,{\Phi }_2\text{and}{\Phi }_3$ in anexperiment of photo-electric effect is plotted as shown in the figure.Which of the following statement(s) is correct? [Here $\lambda$ is the wavelength of the incident ray].

The temperature at which the root mean square velocity of a molecule will be doubled than at ${100}^{\circ }C$

The initial mass of a rocket is $1000\text{kg}$. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20{\text{ms}}^{-2}$. the gases come out at a relative speed of $500{\text{ms}}^{-1}$ with respect to the rocket : [use $g=10{\text{ms}}^{-2}$]

A particle travels along the X-axis. Its velocity time graph is shown above.

In which direction was the particle headed at t = 16 sec?

The radius of the nucleus is proportional to $\left(A\text{is the mass number}\right)$

From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of disc about a perpendicular axis, passing through the centre?

Consider two point charges, $\frac{q}{3}$ and $-\frac{2q}{3}$ at point $\text{B}$ and $\text{C}$ respectively as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and $\angle CAB={60}^{\circ }$. The magnitude of force between the charges is

Derive a dimensional formula for

COULOMB'S CONSTANT.

When a dielectric slab is inserted between the plates of one of the two identical capacitors shown in the figure, then

match the following.

$\begin{array}{cc}Column-I& Column-II\\ \left(A\right)ChargeonA& \left(p\right)increases\\ \left(B\right)PotentialdifferenceacrossA& \left(q\right)decreases\\ \left(C\right)PotentialdifferenceacrossB& \left(r\right)remainsconstant\\ \left(D\right)ChargeonB& \left(s\right)willchange\end{array}$

1. undefined
2. undefined
3. undefined
4. undefined

A person is holding a bucket by applying a force of $10N$. He moves a horizontal distance of $5m$ and then climbs up a vertical distance of $10m$. The total work done by him is equal to

The angular velocity of a wheel is 70 rad/sec. If the radius of the wheel is 0.5 m, then linear velocity of the wheel is

A monochromatic light source of intensity 5 mW emits 8 $\times {10}^{15}$ photons per second. This light ejects photo electrons from a metal surface. The stopping potential for this setup is 2.0 V. Calculate the work function of the metal.

If
the photon of the wavelength 150 pm strikes an atom and one of its
inner bound electrons is ejected out with a velocity of 1.5 ×
10⁷
ms^–1,
calculate the energy with which it is bound to the nucleus.

A sonometer wire of density d and radius r is held between two bridges at a distance L apart. The wire has a tension T. The fundamental frequency of the wire will be

The electric potential V at any point in space is given V=20x3 volt, where x is in meter. Calculate the electric intensity at point P(1,0,2).

Seven particles each of mass $m$ are placed at the corners of a cube of side $b$. The co-ordinates of the centre of mass of the system is

Charcteristic of vector

Find out the magnitude of electric field intensity at point $(2,0,0)$ due to a dipole of dipole moment $\overrightarrow{P}=\hat{i}+\sqrt{3}\hat{j}$ kept at origin. Also find the potential at that point.

The wires A and B shown in the figure are made of the same material and have radii $r_A$ and $r_B$ respectively. The block between them has a mass m. When the force F is $\frac{mg}{3}$, one of the wires breaks, then

In the figure ball A is released from rest, when the spring is at its natural length. For the block B of mass M to leave contact with the ground at some stage, the minimum mass of A must be

The work function $(\varphi$) of some metals is listed below.

$[\text{Use}hc=1240\text{eV nm}]$

Steam is passed into $56\text{g}$ of water at ${30}^{\circ }\text{C}$ till the temperature of mixture becomes ${90}^{\circ }\text{C}$. If the latent heat of steam is $536\text{cal/g}$, the mass of the mixture will be:
(Specific heat capacity of water is $1{\text{cal/g}}^{\circ }\text{C}$)

A heat flux of $4000\text{J/s}$ is to be passed through a copper rod of length $10\text{cm}$ and area of cross section $100{\text{cm}}^2$. The thermal conductivity of copper is $400{\text{W/m}}^{\circ }C$. The two ends of the rod must be kept at temperature difference of

The potentiometer wire AB shown in figure (32-E26) is 40 cm long. Where should the free end of the galvanometer be connected on AB so that the galvanometer may show zero deflection ?

figure (32-E26)

A conducting loop of resistance $r$ is placed in a non-uniform magnetic field of strength $B=B_0{t}^3$ perpendicular to the plane of the loop. Find the charge flown in the loop in the time interval $t_0$.

Find the ratio of intensity at $1^{st}$ maximum to intensity at $2^{nd}$ maximum in a single slit diffraction experiment.

A toroid of mean radius $16\text{cm}$ has $1000$ turns of wire closely wounded on a ferromagnetic core of relative permeability $400$. What is the magnetic induction $B$ within the core for a magnetizing current of $1\text{A}$ ?

Three capacitors of capacitances 3μF,9μFand 18μFare connected once in

series and another time in parallel. The ratio of equivalent capacitance in

the two cases will be

A small sphere $B$ of mass $1\text{kg}$ is released from rest in the position shown and swings freely in a vertical plane, first about $O$ and then about the peg $A$ after the cord comes in contact with the peg. The tension in the cord just after it comes in contact with the peg is

[Take $g=10{\text{m/s}}^2$]

A travelling harmonic wave on a string is described by

(a) What are the displacement and velocity of oscillation of a point at x = 1 cm, and t = 1 s? Is this velocity equal to the velocity of wave propagation?

(b) Locate the points of the string which have the same transverse displacements and velocity as the x = 1 cm point at t = 2 s, 5 s and 11 s.

The weight of an object at the center of a planet of radius R is: