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The graph below shows the water needed for plants in a certain time.

Find the equation for the above graph.

Two charges $q_1$ and $q_2$ are placed $30\text{cm}$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\text{cm}$ from $C$ to $D$. The change in the potential energy of the system is $\frac{q_3}{4\pi {ϵ}_0}k$, where $k$ is

A convex lens of focal length 50 cm is cut along the diameter into two identity halves A and B and in the process a layer C of the lens thickness 1 mm is lost. Then the two halves A and B are put together to form a composite lens. Now in front of this composite lens a source of light emitting wavelength $\lambda =6000\stackrel{\circ }{A}$ is placed at a distance of 25 cm as shown in the figure. Behind the lens there is a screen at a distance 50 cm from it. Choose the correct option(s):

The potential energy of a particle executing SHM changes from maximum to minimum in $5\text{s}$. The time period of SHM is:

What should be the radius of an isolated spherical conductor so that it has a capacity of 2μF?

A box $P$ and a coil $Q$ are connected in series with a $10\text{V}$ AC source whose frequency can be varied. Box $P$ contains a capacitance of $1\mu \text{F}$ in series with a resistance of $32\Omega$. Coil $Q$ has a self inductance $4.9\text{mH}$ and a resistance of $68\Omega$. The frequency is adjusted so that the maximum current flows in $P$ and $Q$. Find the value of angular frequency of the source and the maximum current in the circuit, respectively.

Radioactivity ${}^{131}\text{I}$ has a half-life of 8.0 days. A sample containing ${}^{131}\text{I}$ has activity $20\mu \text{Ci}$ (a) What is its activity at t = 4.0 days ? (b) What is its decay constant at t = 4.0 days ?

_{If the wavelength of the first line in the Balmer series is 656nm. Calculate the wavelength of the second line and the limiting line in Balmer series.}

At 27${}^{\circ }$ C, the ratio of rms velocities of ozone to oxygen is

In a hydrogen atom, an electron of mass $m$ and charge $e$ revolves in an orbit of radius $r$ making $n$ revolutions per second. If the mass of hydrogen nucleus is $M$, the magnetic moment associated with the orbital motion of electron is

Current sensitivity of a moving coil galvanometer is $5\left(\frac{\text{div}}{\text{mA}}\right)$ and its voltage sensitivity (angular deflection per unit voltage applied) is $20\left(\frac{\text{div}}{\text{V}}\right).$ The resistance of the galvanometer is-

If a cricket player can throw a ball to a maximum horizontal range of $60m$, what is the maximum vertical height (in $m$) to which he can throw?

________ is being used in the given scenarios to reduce friction.

Find the acceleration of $\text{B}$, if the acceleration of wedge $\text{A}$ is $a$ as shown in figure.

Two neighbouring coils $\text{A}$ and $\text{B}$ have a mutual inductance of $20\text{mH}$. The current flowing through $\text{A}$ is given by $i=3t^2-4t+6$. The induced emf at $t=2\text{s}$ in coil $\text{B}$ is-

Compute
the typical de Broglie wavelength of an electron in a metal at 27 ºC
and compare it with the mean separation between two electrons in a
metal which is given to be about 2 × 10⁻¹⁰
m.

[Note:
Exercises 11.35 and 11.36 reveal that
while the wave-packets associated with gaseous molecules under
ordinary conditions are non-overlapping, the electron wave-packets in
a metal strongly overlap with one another. This suggests that whereas
molecules in an ordinary gas can be distinguished apart, electrons in
a metal cannot be distinguished apart from one another. This
indistinguishibility has many fundamental implications which you will
explore in more advanced Physics courses.]

The amplitude and the periodic time of a S.H.M. are 5cm and 6sec respectively. At a distance of 2.5 cm away from the mean position, the phase will be

A spherical cavity of radius $R$ is cut from a non-conducting sphere of volulme charge density $\rho {\text{C/m}}^3$ as shown in figure. Find the magnitude of the net electric field at point $\text{P}$.

A long wire carrying a current of 20A is fixed. Another long wire AB is to be balanced mid-air a distance 2cm. Find the magnitude of the current in AB. Also find the angular frequency of SHM. If AB is slightly disturbed from this position. Given the mass per unit length of the wires is ${10}^{-6}kg/m$

A jet airplane travelling at a speed of $500{\text{km h}}^{-1}$ ejects its products of combustion at the speed of $1500{\text{km h}}^{-1}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

An inductive circuit contains resistance of $1\Omega$ and an inductance of $2.0\text{H}$. If an $AC$ voltage of $120\text{V}$ and frequency $60\text{Hz}$ is applied to this circuit, the current would be nearly

Two identical blocks of weight $W$ are placed one on top of the other as shown in the figure. The upper block is tied to the wall. The coefficient of static friciton between $B$ and the ground is $\mu$ and there is no friction between $A$ and $B$. When $F=\mu W$ force is applied on the lower block as shown, the tension in the string will be

A larger tank with a nozzle attached contains three immiscible fluids as shown in figure. Assuming that the changes in $h_1,h_2$ and $h_3$ are negligible, the discharge velocity at this instant is

The figure represents the voltage applied across a pure inductor. The diagram which correctly represent the variation of current $\left(i\right)$ with time $\left(t\right)$ is given by -

The derivative of $e^{\ln \left(\sin x\right)}$ with respect to $x$ where $x\in (0,\frac{\pi }{2}),$ is

The force on a particle is directed along an $x$ axis and given by

$F=F_0(x/x_0-1).$ Find the work done by the force in moving the particle from $x=0$ to $x=2x_0$.

A particle of mass M moves with constant speed along a circular path of radius r under the action of a force F. Its speed is