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The radius of the first orbit of hydrogen in $0.528\dot{A}$. The radius of second orbit of hydrogen is

The equation of a standing wave in an open organ pipe is given by: $p=16\sin \left(\frac{\pi }{3}x\right)\cos \left(64t\right)$, where symbols have their usual meaning. Here $x$ is in $\text{cm}$, $t$ is in $\text{seconds}$ and the amplitude is given in $\text{cm}$ .Then, the first pressure node is obtained at a distance $x$ from one end. What is the value of $x$?

Draw the speed time graph from the given velocity time graph.

In a situation shown below, if the speed of the tip of the seconds hand is $v\text{m/s}$, find the magnitude of change in its velocity.

A $3\text{kg}$ block collides with a massless spring of spring constant $110\text{N/m}$ attached to a wall. The speed of the block was observed to be $1.4\text{m/s}$ at the moment of collision. The acceleration due to gravity is $9.8{\text{m/s}}^2$. How far does the spring compress if the horizontal surface on which the mass moves is frictionless?

The heat generated by radioactivity within the earth is conducted outward through the oceans. Assuming the average temperature gradient within the solid earth beneath the ocean to be ${0.07}^{\circ }{C}^{-1}$ and the average thermal conductivity $0.2cal{m}^{-1}{s}^{-1}{C}^{-1}$, determine the rate of heat transfer per square meter. Radius of the earth = 6400 km. Further, determine the quantity of heat transferred through the earth's surface each day.

A square loop of side 4 cm is lying on a horizontal table. A uniform magnetic field of 0.5 T is directed downwards at an angle of ${60}^o$ to the vertical as shown in Fig. 25.3. If the field increases from zero to its final value in 0.2 s, the emf induced in the loop will be

A particle of mass $0.1\text{kg}$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$, then its velocity at $x=12\text{m}$ is

What is the velocity of block B?

A man in a balloon, throws a stone downwards with speed of 5 m/s with tespect ot balloon. The balloon is moving upwards with a constant acceleration of $5m/s^2$ . Then velocity of the stone relative to the man after 2 second is

Find the value of $\cos (\frac{3\pi }{2}+x)\cos (2\pi +x)\left[\cot \right(\frac{3\pi }{2}-x)+\cot (2\pi +x\left)\right]$.

Given, ${\sin }^{2}x+{\cos }^{2}x=1$

The position vector of a particle is $\overrightarrow{r}=\left(acos\omega t\right)\hat{i}+\left(asin\omega t\right)\hat{j}$. The velocity of the particle is

A box of mass $\text{8 kg}$ is placed on a rough inclined plane of angle $\theta$ with horizontal. Its downward motion can be prevented by applying an upward pull $F$ and it can be made to slide upwards by applying a force $2F$. The coefficient of friction between the box and the inclined plane is

Plot the acceleration - time graph of the velocity - time graph given in the figure.

According to photon theory of light which of the following physical quantities associated with a photon do not/does not change as it collides with an electron in vacuum

A particle of mass $m$ is projected from the ground with initial linear momentum $p$ (magnitude) so as to have maximum possible range. Its minimum kinetic energy will be

Figure shows part of a circuit. Energy stored in $2\mu F$ capacitor at steady state is:

Force constant of a spring is $100\text{N/m}$. If both the blocks of mass $10\text{kg}$ and $12\text{kg}$ attached with spring and string are at rest. Then find the extension in spring. Take $g=10{\text{m/s}}^2$.

The radius of a nucleus of a mass number A is directly proportional to

A body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same, then which of the following statement is true

If G is the universal gravitational constant and $\rho$ is the uniform density of a spherical planet. Then shortest possible period of rotation around a planet can be

A square plate of edge 'd' and a circular disc of diameter 'd' are placed touching each other at the midpoint of an edge of the plate as shown in figure. Locate the centre of mass of the combination, assuming same mass per unit area for the two plates.

Two cars $A$ and $B$ are $5\text{km}$ apart on a line joining South to North. Car $A$ further North is streaming west at $10\text{km/hr}$ and Car $B$ is streaming North at $10\text{km/hr}$. What is their closest distance of approach?

A parallel plate capacitor contains a mica sheet (thickness $={10}^{-3}m$) and a sheet of fibre (thickness $=0.5\times {10}^{-3}m$). The dielectric constant of mica is 8 and that of fibre is 2.5. Assuming that the fibre breaks down when subjected to an electric field of $6.4\times {10}^{6}V/m$, find the maximum safe voltage that can be applied to the capacitor.

A ball is tossed up with an initial speed of $24\text{m/s}$. How high up will it go?

A NPN transistor conducts when

A particle is thrown upwards with speed $v_0$. Find its speed when it reaches $2/3^{rd}$ of the maximum height.

The power factor of the circuit shown below is $1/\sqrt{2}.$ The capacitance of the circuit is equal to

When a cylindrical tube is dipped vertically into a liquid, the angle of contact is ${140}^{\circ }$. When the tube is dipped with an inclination of ${40}^{\circ }$, the angle of contact is:

As shown in figure, two light springs of force constant $300\text{N/m}$ and $600\text{N/m}$ oscillate a block of mass $10\text{kg}$. Find the effective force constant.

A cyclic process for $1\text{mole}$ of an ideal gas is shown in the $V-T$ diagram. The work done in $AB,BC$ and $CA$ respectively is

A force $(3\hat{i}+4\hat{j})N$ acts on a body and displaces it by $(3\hat{i}+4\hat{j})$ meters. The work done by the force is

(Given that formula for work done is $W=\overrightarrow{F}.\overrightarrow{s})$

The position of an elevator varies with time according to this function

$p\left(t\right)=x^2+2x+3$

What will be the velocity of the elevator at time t = 4 secs

The Young’s modulus of a wire of length L and radius r is $\frac{YN}{m^2}$. If the length and radius are reduced to $\frac{L}{2}$ and $\frac{r}{2}$, then its Young's modulus will be

Four particles of masses $1\text{g},2\text{g},3\text{g}$ and $4\text{g}$ are kept at points $(0,0),(0,3\text{cm}),(3\text{cm},3\text{cm}),(3\text{cm},0\text{cm})$ respectively. Find the moment of inertia of the system of particles (in ${\text{g-cm}}^2$) about $y$ axis.

A spherical drop of water has radius $r\text{m}$. If surface tension of water is $70\times {10}^{-3}\text{N/m}$ and the pressure difference between inside and outside of the spherical drop is $280{\text{N/m}}^2$. Find the value of $r$.

A $\text{U}-$ shaped wire $abcd$ of length $30\text{cm}$ is placed before a concave mirror having radius of curvature $20\text{cm}$. Find the total length of the image of wire.

A piece of copper and the other of germanium are cooled from the room temperature to 80 K, then which of the following would be a correct statement

Find the reading of the spring balance if $M$ is in equilibrium. Assume all surfaces to be smooth. Take $g=10{\text{m/s}}^2$.

A particle loses $25\%$ of its kinetic energy during head on collision with another identical particle initially at rest. The coefficient of restitution will be

A uniformly tapering vessel is filled with a liquid of density 900 $kg/m^3$. The force that acts on the base of the vessel due to the liquid is (g=$10m{s}^{-2}$)

The sound from a very high burst of fireworks takes 5 s to arrive at the observer. The burst occurs 1662 m above the observer and travels vertically through two stratifier layers of air, the top one of thickness

$d_1$ at $0^{\circ }C$ and the bottom one of thickness $d_2$ at ${20}^{\circ }C$. Then (assume velocity of sound at $0^{\circ }C$ is 330 m/s)

You are supplied with three identical rods of same length and mass . If the length of each rod is $2\pi$. Two of them are converted into rings and then placed over the third rod as shown in figure. If point A is considered as origin of the coordinates system, the coordinate of the centre of mass will be (you may assume AB as x - axis of the coordinate system)