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There are two metallic loops of radii $0.2\text{m}$ and $0.5\text{m}$. The smaller loop is placed within the bigger one. Calculate the magnitude of the magnetic flux through the bigger loop, if the field is directed into the page of the loop and enclosed by the smaller loop. The strength of the magnetic field is $2.4\text{T}$.

A liquid with speed $v$ through a horizontal pipe of cross sectional area $A$ enters into another pipe of double the area of cross-section. The speed of the liquid in the second pipe will be

One of the following wavelengths is absent and the rest are present in the X-rays coming from a Coolidge tube. Which one is the absent wavelength?

An object is projected with a velocity of $20\text{m/s}$ making an angle of ${45}^{\circ }$ with horizontal. The equation for the trajectory is $h=Ax-B{x}^2$ where $h$ is height, $x$ is horizontal distance, A and B are constants. The ratio A : B has value of $(g=10m{s}^{-2})$

A student is performing the experiment of Resonance Column. The diameter of the column tube is $4cm$. The frequency of the tuning fork is $500Hz$. The air temperature is $38{}^{\circ }C$ in which the speed of sound is $340m/s$. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is

As shown in the figure, from a uniform rectangular sheet, a triangular sheet is removed from one edge. The shift of the centre of mass (with respect to $\text{O}$) is

Two small boats are $10\text{m}$ apart on a lake. Each boat pops up and down with a period of $4.0\text{sec}$ due to wave motion on the surface of water. When one boat is at its highest point, the other boat is at its lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is,

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A particle of mass $m$ is projected vertically upwards from point $\Delta$ on the ground. The ratio of potential energy at point $A$ and potential energy at $B$ is

A solid sphere is in pure rolling motion on an inclined surface having inclination $\theta$

In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is $1:10.$ If the power to the consumers has to be supplied at $200V,$ the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is

A bowl whose bottom has a round hole of diameter $1\text{mm}$ is filled with water. Assuming that surface tension acts only at hole, find the maximum height (in $\text{cm}$) up to which water can be filled in the vessel without leakage. (Given, surface tension of water $=75\times {10}^{-3}{\text{Nm}}^{-1},g=10{\text{ms}}^{-2}$ and density of water $1000{\text{kg/m}}^3$).
cm.

A particle of mass $m$ is dropped from a height $h$ above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$ . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is

Three blocks of masses $m_1$, $m_2$ and $m_3$ are connected by massless strings as shown in the figure and placed on a frictionless table. They are pulled with a force $T_3=40N$. The tension $T_2$ will be: (Given $m_1=10kg,m_2=6kg$ and $m_3=4kg$)

A body $A$ starts from rest with an acceleration $a_A$. After 2 seconds, another body $B$ starts from rest with an acceleration $a_B$. If they travel equal distances in the $5^{th}$ second, after the start of $A$, then the ratio $a_A:a_B$ is equal to

A mixture of $1$ mole of nitrogen and $1$ mole of hydrogen is in a container at room temperature. The ratio of root mean square speed of hydrogen and nitrogen molecules is

A ball is projected perpendicularly from an inclined plane of inclination $\theta$ from horizontal, with velocity ${}^{\prime }{u}^{\prime }$ as shown in figure. The time after which the projectile is making angle ${45}^{\circ }$ with the inclined plane is

The position vector of three particles of mass $m_1=3\text{kg},m_2=4\text{kg}$ and $m_3=1\text{kg}$ are $\overrightarrow{r_1}=(2\hat{i}+\hat{j}+3\hat{k})\text{m},\overrightarrow{r_2}=(\hat{i}-3\hat{j}+2\hat{k})\text{m}$ and $\overrightarrow{r_3}=(3\hat{i}-2\hat{j}-\hat{k})\text{m}$ respectively. Find the position vector of centre of mass of the system of particles.

Two monoatomic ideal gases 1 and 2 of molecular masses $m_1$ and $m_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to gas 2 is given by

Alternating
current can not be measured by dc ammeter because

[AIEEE 2004]

Choose the graph that represents the variation of potential $\left(V\right)$ versus distance from the centre of ring along its axis $\left(r\right)$ for a uniform ring of change $Q$.

A small ball, of mass $m$, is thrown upward with a velocity $u$, from the ground. The ball experiences a resistive force $mk{v}^2$ where $v$ is its speed. The maximum height attained by the ball is :

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440\text{Hz}$ to $480\text{Hz}$ when it gets reflected from the wall. If the speed of sound in air is $345\text{m/s}$, then speed of the car is

Three rods of the same dimension have thermal conductivities $3K,2K$ and $K$. They are arranged as shown in figure given below, with their ends at ${100}^{\circ }C,{50}^{\circ }C$ and ${20}^{\circ }C$. The temperature of their junction is

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