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The de broglie wavelength of neutrons in thermal equlibrium at temperature $T$ is

Which
of the following potential energy curves in Fig. 6.18 cannot possibly
describe the elastic collision of two billiard balls? Here r
is the
distance between centres of the balls.

If the magnetic field at ‘P’ can be written as $K$ $\tan \left(\frac{\alpha }{2}\right)$, then $K$ is

Two identical masses are connected to identical springs of spring constant $K$ as shown in the figure. Find the time period of small oscillations.

The pulley is given an acceleration $a_0=2{\text{m/s}}^2$ starting from rest. A cable is connected to a block $A$ of mass $50\text{kg}$ as shown. Neglect the mass of the pulley. If $\mu =0.3$ between the block and the floor, then the tension in the cable is:

A ball is dropped from a height. If the maximum percentage errors in measurement of the height and the time are $e_1$ and $e_2$ respectively, then maximum percentage error in the estimation of $g$ is

Number of molecules in a volume of $4{\text{cm}}^3$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2\text{cm}$ of mercury is close to ?

(Given, mean kinetic energy of a molecule (at $T$) is $4\times {10}^{-14}\text{erg},g=980{\text{cm/s}}^2$, density of mercury $=13.6{\text{g/cm}}^3$)

A coil of resistance $40\Omega$ is connected to a galvanometer of $160\Omega$ resistance. The coil has radius of $6\text{mm}$ and $100\text{turns}$. This coil is placed between the poles of a magnet such that the magnetic field is perpendicular to plane of the coil. If the coil is dragged out of this magnetic field instantaneously, a total charge of $32\mu \text{C}$ flows through the galvanometer. The magnitude of magnetic field is:

A balloon which always remains spherical is being inflated by pumping in 10 cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius in 15 cms.

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v\left(x\right)=\beta x^{-2n}$.Where, $\beta$ and $n$ are constants and $x$ is the position of the particle. Find The acceleration of the particle as a function of $x$, if $n=2$

If the dimension of liquid drop and bubble of same liquid solution is same, then find the ratio of excess pressure inside liquid drop to the excess pressure inside bubble?

Aheating
element using nichrome connected to a 230 V supply draws an initial
current of 3.2 A which settles after a few seconds toa steady
value of 2.8 A. What is the steady temperature of the heating element
if the room temperature is 27.0 °C? Temperature coefficient of
resistance of nichrome averaged over the temperature range involved
is 1.70 × 10⁻⁴ °C ⁻¹.

The charge flowing through a resistance R varies with time as $Q=2t-8t^2$. The total heat produced in the resistance is
$(\text{for}0\le t\le \frac{1}{8})$

Calculate the steady-state current in the 2$\Omega$ resistor shown. Theinternal resistance of the battery is negligible and the capacitance of the capacitor is 0.2 $\mu F$.

The positive point charges, each equal to +q, are placed at corners A, B and C of a square of side a. The magnitude of the force experienced by a point charge +Q placed at corner D is

Resistor of resistance of $6\Omega$ each are connected in the manner shown in figure. With the current $0.5\text{A}$, the potential difference $V_A-V_B$

Work done when a force $\overrightarrow{F}=(\hat{i}+2\hat{j}+3\hat{k})\text{N}$ acting on a particle displaces it from the point $r_1=(\hat{i}+\hat{j}+\hat{k})$ to the point $r_2=(\hat{i}-\hat{j}+2\hat{k})$ is

34. One coulomb of charge is passed through a solution of $AgN{O}_3$ and $CuS{O}_4$ connected in series and the concentration of two solutions are in the ratio 1:2. The ratio of weight of Ag and Cu deposited on Pt electrode is

(1) 107.9: 63.54

(2) 54 :31.77

(3) 107.9 : 31.77

(4) 54:63.54

For the wave shown in the figure, write the equation of the wave if its position is shown at $t=0$ speed of wave is 200 m/s.

The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_1$ and $r_2$ ($r_1=1.5r_2)$ through $1\text{K}$ are in the ratio :

Five similar condenser plates, each of area $A$ are placed at equal distance $d$ apart and are connected to source voltage $V$ as shown in the following diagram. The charge on plates $1$ and $4$ will be:

For the body shown in the figure:


Statement $1:I_z=I_x+I_y$
Statement $2:I_x=I_z+I_y$ and $I_y=I_x+I_z$
where $x$, $y$ and $z$ are the axes of rotation of the body.
Choose the correct option.

The ammeter, voltmeter and, resistors R₁ and R₂ connected in the circuit as shown below have been checked and found to be correct.







On plugging the key, the voltmeter reads 4.5 V but the ammeter reads 1.5 A. This is most likely because the wires joined to:

(1) resistor R₁ and loose

(2) resistor R₂ are loose

(3) both the resistors R₁ and R₁ are loose

(4) ammeter terminals are loose