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It
is desired to measure the magnitude of field between the poles of a
powerful loud speaker magnet. A small flat search coil of area 2 cm²
with 25 closely wound turns, is positioned normal to the field
direction, and then quickly snatched out of the field region.
Equivalently, one can give it a quick 90° turn to bring its plane
parallel to the field direction). The total charge flown in the coil
(measured by a ballistic galvanometer connected to coil) is 7.5 mC.
The combined resistance of the coil and the galvanometer is 0.50 Ω.
Estimate the field strength of magnet.

A man of mass $m$ stands on a crate of mass $M$. He pulls on a light rope passing over a smooth light pulley. The other end of the rope is attached to the crate. For the system to be in equilibrium, the force exerted by the man on the rope will be

A solid cylinder is kept on one edge of a plank of same mass and length 25 m placed on a smooth surface as shown in the figure. The coefficient of friction between the cylinder and the plank is 0.5. The plank is given an initial velocity of 20 m/s towards right. Find the time (in sec) after which plank and cylinder will separate. $(g=10m/s^2)$

A concrete slab has a length of 10 m on a winter night when the temperature is $0^{\circ }C$. Find the length of the slab on a summer day when the temperature is ${35}^{\circ }C$. The coefficient of linear expansion of concrete is $1.0\times {10}^{-5}{}^{\circ }{C}^{-1}$

What is the angle of banking necessary for a curved frictionless road of radius $30\text{m}$ for safe driving at a speed of $20\text{m/s}$? (Consider value of $g=10{\text{m/s}}^2$)

A particle is moving with velocity $\overrightarrow{V}=4x\hat{i}+4y\hat{j}$, then general equation for path of particle is

The velocity of a body of mass $2kg$ varies according to the equation $v=(10S–3)m/s$ where $S$ is the displacement of the body (in $m$). Find the force acting on the body at the instant when it has undergone a displacement of $2m$.

The string shown in the figure is passing over a smooth pulley rigidly attached to the trolley $A$. The speed of the trolley is constant and equal to $v_A$. Speed and magnitude of acceleration of block $B$ at the instant shown in the figure is $v_B$ and $a_B$ respectively, then

A particle experiences constant acceleration for $20$ seconds after starting from rest. If it travels a distance $s_1$ in the first $10$ seconds and distance $s_2$ in the next $10$ seconds, then

Find the magnetic field $B$ at the center of square loop of side $a$ carrying a current $I$.

A highly conducting solid sphere of radius $R$ , density $\rho$ and specific heat $s$ is kept in an evacuated chamber. A parallel beam of thermal radiation of intensity $I$ is incident on its surface.
Consider the sphere to be a perfectly black body and its temperature at certain instant $t=0$ is considered as $T_0$ [Take Stefan's constant as $\sigma$]
The maximum attainable temperature of the sphere is

Two identical sheets of the same metallic foil of the area $A$ are separated by a distance $d$, and charged by a battery of emf $E$. Keeping the charge constant, the separation is increased by $l$. Then, the new capacitance and potential difference will be

Following figure shows on adiabatic cylindrical container of volume V_o divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas is at pressure P₁ and temperature T₁ in left part and gas at pressure P₂ and temperature T₂ in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

Consider a simple RC circuit as shown in Figure 1





Process 1 : In the circuit the switch $S$ is closed at $t=0$ and the capacitor is fully charged to voltage $V_e$ (i.e. charging continues for time $T>>RC$ ). In the process some dissipation ($E_D$) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is $E_c$.



Process 2 :

In a different process the voltage is first set to $\frac{V_0}{3}$ and maintained for a charging time T>>RC. Then the voltage is raised to $\frac{2V_0}{3}$ without discharging the capacitor and again maintained for a time $T>>RC$. The process is repeated one more time by raising the voltage to $V_0$ and the capacitor is charged to the same final voltage $V_0$ as in Process $1.$

These two processes are depicted in Figure 2.





In Process $2,$ total energy dissipated across the resistance $E_D$ is

A line charge λ per
unit length is lodged uniformly onto the rim of a wheel of mass M
and radius R. The wheel has light non-conducting spokes
and is free to rotate without friction about its axis (Fig. 6.22). A
uniform magnetic field extends over a circular region within the rim.
It is given by,

B = − B₀ k (r ≤ a;
a < R)

= 0 (otherwise)

What is the angular
velocity of the wheel after the field is suddenly switched off?

A simple pendulum with a bob of mass $m=1\text{kg}$, charge $q=5\mu \text{C}$ and string length $l=1\text{m}$ is given a horizontal velocity $u$ in a uniform electric field $E=2\times {10}^6\text{V/m}$ at its bottom most point $\text{A}$ as shown in figure. It is given that the speed $u$ is such that the string slacks at point $\text{C}$. Find the speed $u$.

[Take $g=10{\text{m/s}}^2$]

If $1000\alpha -$particles scattered at an angle of ${180}^{\circ }$ targeted at an atom, then the number of $\alpha -$particles scattering at ${90}^{\circ }$ will be -

A point charge is placed at the origin O. Work done in taking another point charge -Q from the point A(0, a) to another point B(a, 0) along the straight path AB is

An electron is released from the origin at a place where a uniform electric field $E$ and a uniform magnetic field $B$ exist along the negative $y$-axis and the negative $z$-axis respectively. Find the displacement of the electron along the $y$-axis when its velocity becomes perpendicular to the electric field for the first time. (Take $E=20\text{V/m}$ and $B=0.5\text{mT}$, charge of electron $e=1.6\times {10}^{-19}\text{C}$ , Mass of electron $m={10}^{-30}\text{kg}$)