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1. 8

When a photon of wavelength $60\text{nm}$ is absorbed by a hydrogen atom, photo-ionization of the atom occurs. The minimum kinetic energy of the emitted electron will be,

The rear side of a truck is open and a box of mass $20\text{kg}$ is placed on the truck $4\text{m}$ away from the open end. The coefficient of friction between the box and the surface is $0.15$. The truck starts from rest with an acceleration of $2{\text{m s}}^{-2}$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to (take $g=10m{s}^{-2}$)

The forces F₁, F_2, and F₃ are acting on a particle of mass m, such that F₂ and F₃ are mutually perpendicular and under the effect of F₁, F_2, and F₃ , the particle remains stationary. What will be the acceleration of the particle, if the force F₁ is removed?

A lead bar of length $50\text{cm}$ and square cross-section of side $5\text{cm}$ is fixed to a vertical wall as shown in figure. A massless tank is suspended from the end of the bar with the help of a massless rope. The tank is slowly filled with mercury at room temperature. Find the level of mercury in the tank so that the end of the bar deviates by $1\text{mm}$.
[Take modulus of rigidity for lead as $5.6\text{Gpa}$ and area of base of cylindrical tank as $0.42{\text{m}}^2;{\rho }_{Hg}=13600{\text{kg/m}}^3\&g=9.8{\text{m/s}}^2$]

Which of the following is the correct relation for the first principal focal length of a single spherical surface?

A wire loop enclosing a semicircle of radius $R$ is located on the boundary of a uniform magnetic field $B$ . At the moment $t=0$ , the loop is set into rotation with constant angular acceleration α about an axis $O$ . The clockwise emf direction is taken to be positive and the magnitude of variation of emf as a function of time is denoted by E . If $t_1$ and $t_2$ are the time required to complete first half and second half circle respectively then, which of of the following options are correct?



($E_n$ is the inducede emf produced in nth half rotation.)

In the circuit shown in figure, the sum of charges on both capacitors at steady state will be:

If I place a random arrangement of dielectrics like this in my capacitor, how do I find my new capacitance?

Two circular coils made of similar wires but of radius $20\text{cm}$ and $40\text{cm}$ are connected in parallel. The ratio of magnetic fields at their centre is -

The velocity $\left(v\right)$ and time $\left(t\right)$ graph of a body in a straight line motion is shown in the figure. The point $S$ is at $4.333\text{s}$ seconds. The total distance covered by the body in $6\text{s}$ is:

Find the minimum value of $F$ for which the system is in equilibrium? $[$ Take $g={\text{10 m/s}}^2]$

(i) For the wave on a string described
in Exercise 15.11, do all the points on the string oscillate with the
same (a) frequency, (b) phase, (c) amplitude? Explain your answers.
(ii) What is the amplitude of a point 0.375 m away from one end?

An electric in the first orbit of hydrogen atom, has a binding energy of $13.6\text{eV}$. If an electron in another hydrogen atom is in the $n=3$ state, how much energy is required to ionize it?

Four wires of identical length, diameters and of the same material are stretched on a sonometer wire. If the ratio of their tension is $1:4:9:16$, then the ratio of their fundamental frequencies is

Twelve resistors each of resistance $r$ are connected together so that each lies along the edge of the cube as shown in the figure. The equivalent resistance between points $1$ and $3$ is

The graph in figure given below represents the velocity-time graph of a particle, starting from rest at point $\text{P}$. Find the time when particle will reach point $\text{P}$ again.

When an object is kept at a distance of $30\text{cm}$ from a concave mirror, the image is formed at a distance of $10\text{cm}$. If the object is moved with a speed of $9{\text{cms}}^{-1}$ in horizontal direction, the speed with which the image moves is

Maximum velocity of photo electron emitted is $4.8m{s}^{-1}$ . If $\left[\frac{e}{m}\right]$ ratio of electron is $1.76\times {10}^{11}\left(Ck{g}^{-1}\right)$ then stopping potential is given by

A charged water droplet hangs from ceiling of a room which has a uniform vertically upwards electrical field of strength 4.00 $\times {10}^{5}N{C}^{-1}$ . This field levitates and prevents a droplet of mass 1.0 $\times {10}^{-4}$kg from falling. Can you find the net charge on the droplet?

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$, is given by

A particle of mass $m$ is attached with four identical springs, each of length $l.$ Initially, each spring has tension $F_0$. Neglecting gravity, calculate the time period for small oscillations of the particle along a line perpendicular to the plane of the figure.

1. 7

The magnitude of electric field due to an infinite uniformly charged insulating sheet is 10 N/C at a point which is at a distance 3m away from it. The surface charge density of the sheet will be?

A 50m long train passes over a bridge at a speed if 30km/h. If it takes 36 s to cross the bridge , the length of the bridge is?

There are two charges +1uc and +5uc. what is the ratio of the force acting on them?