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The velocity-time graph of a particle moving in a straight line is as shown in figure. Find the total displacement of the particle during its journey.

The photoelectric threshold wavelength of a certain metal is $3000\stackrel{\circ }{A}$. If the radiation of $2000\stackrel{\circ }{A}$ is incident on the metal

If water be used to construct a barometer, what would be the height of water column at standard atmospheric pressure i.e., 76 cm of mercury? Specific gravity of mercury = 13.6

A particle covers 50 m distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed

A beam of light having wavelengths distributed uniformly between 450 nm to 550 nm passes through a sample of hydrogen gas. wavelength will have the least intensity in the transmitted beam ?

Three charges each of charge ‘q’ are placed at the corners of an equilateral triangle. The fourth charge to be placed at the centre of the triangle so that electrostatic potential energy of the system is zero is

A ray of light is incident at the glass–water interface at an angle i, it emerges finally parallel to the surface of water, then the value of ${\mu }_g$ would be

The upper half of an inclined plane of inclination q is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

A nucleus moving with a velocity $\overrightarrow{v}$ emits an$\alpha$-p article. Let the velocities of the $\alpha$-particle and the remaining nucleus be $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ and their masses be $m_1$, and $m_2$.

A simple pendulum is constructed by hanging a heavy ball by a 5.0 m long string. It undergoes small oscillations. (a) How many oscillations does it make per second ? (b) What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is $1.67m{s}^{-2}$?

What is the vapour pressure of water at ${373}^{\circ }K$?

A mosquito is sitting on an L.P. record disc rotating on a turn table at $33\frac{1}{3}$ revolutions per minute. The distance of the mosquito from the centre of the turn table is 10 cm. Show that the friction coefficient between the record and the mosquito is greater than $\pi \frac{2}{81.}$ Take $g=10m/s^2.$

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of the materials, then

The temperatureof an Ideal Gas is increased from 140K to 560 K. If at 140 K the r.m.s. velocity of the gas molecule is V, at 560 K it becomes

Column- I gives some current distributions and a point P in the space around these current distributions. Column II gives some expressions of magnetic field strength. Match column- I to corresponding field strength at point P given in Column - II.
$\begin{array}{cccc}& \text{Column I}& & \text{Column - II}\\ \text{(A)}& \text{A conducting loop shaped as regular hexagon of side}x\text{,}& \text{(P)}& \frac{3{\mu }_{0}i}{32\pi x}\\ & \text{carrying current i. P is the centriod of hexagon}& & \\ \text{(B)}& \text{A cylinder of inner radius}x\text{and outer radius}3x\text{, carrying}& \text{(Q)}& \frac{\sqrt{3}{\mu }_{0}i}{\pi x}\\ & \text{current i. Point P is at a distance}2x\text{from the axis of the cylinder}& & \\ & \text{the cylinder}& & \\ \text{(C)}& \text{Two coaxial hollow cylinders of radii}x\text{and}2x\text{, each carrying}& \text{(R)}& \frac{{\mu }_{0}i}{2x}\\ & \text{current i, but in opposite direction. P is a point at distance}& & \\ & 1.5x\text{from the axis of the cylinders}& & \\ \text{(D)}& \text{Magnitude field at the centre of an n-sided regular}& \text{(S)}& \frac{{\mu }_{0}i}{3\pi x}\\ & \text{polygon of circum circle of radius}x\text{, carrying current}& & \\ & \text{i,}\text{take}n\to \infty ,\text{P is centroid of the polygon}& \text{(T)}& \text{Zero}\end{array}$

A capacitor of $2\mu F$ is charged as shown in the diagram. When the switch $S$ is turned to position $2$, the percentage of its stored energy dissipated is

Find the least count of a screw gauge whose least count of linear scale is 1 mm and the circular scale is divided in 50 divisions and 2 entire rotations makes to 1 division on linear scale.

According to the classical wave picture of light, how would the current versus potential (between the plates) graph vary upon varying intensity?

Two points on string are being observed as a travelling wave passes from them. The points are at $x_1=0$ and $x_2=1\text{m}$, the transverse motions of two points are found to be as follows $y_1=\text{A sin}\left(3\pi t\right)$ and $y_2=\text{A sin}(3\pi t+\frac{\pi }{8})$; t is in seconds and y in metre. Mark the correct option(s)

A current 4 A flows in a coil when connected to a 12 V dc source. If the same coil is connected to a 12 V ac source $(\omega =50rad{s}^{-1})$ a current of 2.4 A flows in the circuit. The inductance of the coil is

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

A very long wire of cross section radius a carry current such that its current density is $J=J_{0}r$. $J_0$ is constant and $r$ is distance from axis of wire. Magnetic field as a function of $r$ is best represented by

A charge q is placed at the center of the line joining two equal charges Q. The system of three charges will be in equilibrium if q is equal to

The potential energy U in joule of a particle of mass 1 kg moving the x-y plane obeys the law U = 3x + 4y, where (x, y) are the co-ordinates of the particle in meter. If the particle is at rest at (6, 4) at time t = 0 then:

In the graph shown below, find the amount of work done.

Four identical samples of an ideal gas are taken along the paths $A,B,C$ and $D$ from state $1$ to state $2$ as shown in the $PV$ indicator diagram. Let $Q,W$ and $\Delta U$ represent the heat supplied, work done and change in internal energy of the gas respectively. Choose the correct option among the following :

Two particles each of mass $5\text{kg}$ are attached to the two ends of a light string of length $15\text{cm}$ which passes through a hole at the center of a table. One particle describes a circle on the table with angular velocity ${\omega }_1=2\text{rad/sec}$ and the other describes a circle as a conical pendulum with angular velocity ${\omega }_2=3\text{rad/sec}$ below the table as shown in the figure. If $l_1$ and $l_2$ are the lengths of the portion of the string above and below the table, then the ratio of $l_1$ and $l_2$ is

Under forced oscillation, the phase of the harmonic motion of the particle and phase of driving force

A particle moves on the x-axis and its velocity varies with time as $v\left(t\right)=t-t^2$. Find the time instant when the particle come back to starting point. Also find the distance travelled till then.

The position vector of $P$ is $4\hat{i}+3\hat{j}$ and the position vector of $Q$ is $-2\hat{i}+5\hat{j}$. The vector $2\overrightarrow{PQ}$ is

a balloon filled with an ideal gas is taken from the surface of the sea deep to a depth of 100m what will be its volume in terms of its original volume?

Sources separated by $20\text{m}$ vibrate according to the equation $y_1=0.06\sin \pi t$ and $y_2=0.02\sin \pi t.$ They send out waves along a rod with speed $3\text{m/s}$. What is the equation of motion of a particle $12\text{m}$ from the first source and $8\text{m}$ from the second? Given $y_1,y_2$ are in metres.

When a ball is thrown up vertically with velocity $v_0,$ it reaches a maximum height of $h$. If one wishes to triple the maximum height, then the ball should be thrown with velocity.

Actually I don't understand when the tension in the light rope becomes zero and if there is a rope in which we apply force on both sides if one side we apply 100N and other side we apply 40N how come the tension here becomes 40N?????

A uniform ring of mass M and radius R is placed directly above a uniform sphere of mass 8 M and of same radius R. The centre of the ring is at a distance of $d=\sqrt{3}R$from the centre of the sphere. The gravitational attraction between the sphere and the ring is

Here are three displacements, each measured in meters:

$\overrightarrow{d_1}=4\hat{i}+5\hat{j}-6\hat{k},\overrightarrow{d_2}=-1\hat{i}+2\hat{j}+3\hat{k},$ and $\overrightarrow{d_3}=4\hat{i}+3\hat{j}+2\hat{k}$

What is $\overrightarrow{r}=\overrightarrow{d_1}-\overrightarrow{d_2}+\overrightarrow{d_3}$?

What is electric potential?

What direction must you swim at to cross the river in minimum time given the crocodiles have left and your maximum velocity is $5\frac{Km}{hr}$ and the velocity of river is $3\frac{Km}{hr}$ in the west direction.

An aluminium measuring rod, which is correct at $5^{\circ }\text{C}$ measures the length of a line as $80\text{cm}$ at ${45}^{\circ }\text{C}$. If thermal coefficient of linear expansion of aluminium is $2.50\times {10}^{-5}{/}^{\circ }\text{C}$, the correct length of the line is

Four massless springs whose force constants are $2k,2k,k$ and $2k$, respectively, are attached to a mass $M$ kept on a frictionless horizontal plane (as shown in figure). If the other ends of the springs are fixed and the mass $M$ is displaced , then the frequency of oscillation of the system is

Two block $A$ and $B$ of mass $10\text{kg}$ and $20\text{kg}$ respectively, are arranged as shown in figure on a smooth horizontal surface. A constant force $F=60\text{N}$ acts on block $A$. Find the minimum coefficient of static friction (${\mu }_{\text{min}}$) so that both the block moves together without slipping? Take $g=10{\text{m/s}}^2$.

Find the moment of inertia of ring having mass $2\text{kg}$ and radius $1\text{m}$ about an axis passing along the diameter of the ring.

A rod of length $L$ is placed along the $x-$ axis between $x=0$ and $x=L$. The linear density (mass/length) $\lambda$ of the rod varies with the distance $x$ from the origin as $\lambda =k{x}^2$. Here $k$ is a positive constant. Find the position of the centre of mass of this rod.