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A single strain gauge of gauge factor $2$ is used in a wheatstone bridge in a quarter bridge arrangement where each resistance is $120\Omega$. If the bridge exciting voltage is $10cos1000tV$ and the gauge is subjected to sinusoidally varying strain of $500\mu m/m$ peak value and a frequency of $20Hz$. Then the equation for the output voltage as observed on a CRO (assuming infinite impedance for the CRO) is

A man of mass $62\text{kg}$ jumps up a staircase of $65$ steps in $12\text{s}.$ If the height of each step is $20\text{cm}$. Find his power.



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

Three liquids of densities ${\rho }_1,{\rho }_2$ and ${\rho }_3$(with ${\rho }_1>{\rho }_2>{\rho }_3$) having the same value of surface tension $\mathrm{T\; and}$ rise to the same height in three identical capillaries. The angles of contact ${\theta }_1,{\theta }_2$ and ${\theta }_3$ obey

The $\text{B-H}$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with $1000\text{turns/cm}$. The current that should be passed in the solenoid to demagnetize a ferromagnet completely is:

A block of mass $m$ is connected to another block of mass $M$ by a massless spring constant $k$, the blocks are kept on a smooth horizontal plane and are at rest. The spring is unstretched when a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the maximum extension of the spring.

Determine the period of oscillation of $200\text{g}$ of $Hg$ in a bent U-tube whose right arm forms an angle ${30}^{\circ }$ with the vertical as shown. The cross-sectional area of the tube is $0.5{\text{cm}}^2$. Neglect viscosity and density of mercury is $13.6{\text{g/cm}}^3$

The rms value of the electric field of the light coming from sun is 720 N/C. The average energy density of the EM wave is

A glass marble whose mass is $200gm$, falls from a height of $2.5m$ and rebounds to a height of $1.6m$. Find the change in momentum due to its fall.

Two point charges $q_1\left(\sqrt{10}\mu \text{C}\right)$ and $q_2(-25\mu \text{C})$ are placed on the x-axis at $x=1\text{m}$ and $x=4\text{m}$ respectively.The electric field in $\left(\text{V/m}\right)$ at a point $y=3\text{m}$ on $y-$axis is



$[\text{Take}\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9{\text{Nm}}^2{\text{C}}^{-2}]$

The string, the spring and the pulley shown in figure (12-E9) are light. Find the time period of the mass m.

A hydrogen atom in ground state absorbs $10.2\text{eV}$ of energy. The orbital angular momentum of the electron is increased by

The intensity of gamma radiation from a given source is $I$ on passing through $36\text{mm}$ of lead it is reduced to $\frac{I}{8}$. The thickness of lead which will reduce the intensity to $\frac{I}{2}$ will be-

A body, acted upon by a force of $50N$ is displaced through a distance $10$ meter in a direction making an angle of ${60}^{\circ }$ with the force. The work done by the force be

Surface mass density of a semicircular disk varies with position as $\sigma ={\sigma }_0\frac{r}{R}$ where ${\sigma }_0$ is constant, $R$ is the radius of the disc and $r$ is measured from the centre of the disc. Find the COM of the disc.

The electric field in a region is given by $\overrightarrow{E}=\alpha x\hat{i}$. Here, $\alpha$ is a positive constant of proper dimension. Find the total flux passing through a cube bounded by the coordinates, $x=l,x=2l,y=0,y=l,z=0,z=l.$

The trigonometric equation $\frac{1-\sin \theta }{1+\sin \theta }$ is equal to

[Given, ${\sin }^2\theta +{\cos }^2\theta =1$]

Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in

If the reference particle P moves in uniform circular motion, its projection along a diameter of the circle executes

Three blocks A, B and C are kept as shown in the figure. The coefficient of friction between A and B is 0.2, B and C is 0.1, C and between C and ground is 0.0. The masses of A, B and C are 3 kg, 2kg and 1 kg respectively, A is given a horizontal velocity 2 m/s. A, B and C always remain in contact. Find (in J) the magnitude of total work done by friction.

$K_f-K_i=W_{friction}$ (K= Kinetic energy)

If the sound level in a room is increased from 50 dB to 60 dB, by what factor is the pressure amplitude increased?

Block A of mass $35\text{kg}$ is resting on a frictionless floor. Another block B of mass $7\text{kg}$ is resting on it as shown in the figure. The coefficient of static friction between the blocks is $0.5$ while kinetic friction is $0.4$. If a force of $100\text{N}$ is applied to block B, the acceleration of the block A will be $(g=10{\text{ms}}^{-2}):$

Charge between parallel plates :



Surface charge density is defined as the charge per unit surface area of surface charge distribution. i.e., $\sigma =\frac{q}{S}$



Two large thin metal plates are parallel and close to each other, on their inner faces, the plates have surface charge densities of opposite sign having magnitude of $1.70\times {10}^{-22}{\text{Cm}}^{-2}$ as shown in figure.

[Use ${\epsilon }_0=8.85\times {10}^{-12}{\text{Fm}}^{-1}$]



$\left(ii\right)$The electric field $E$ in the region to the left of plate $\text{A}$ and to the right of plate $\text{B}$ is

Two equal mass objects are moving in a circular path with constant speed as shown in the figure. The collision is elastic everytime. They meet at $A$ again on $n^{th}$ collision, find the value of $n?$



[Assume, collisions are elastic in nature]

A triangular plate is shown in the figure. A force $\overrightarrow{F}=4\hat{i}-3\hat{j}$ is applied at point $P$. The torque acting at point $\text{P}$ with respect to point $\text{O}$ and point $\text{Q}$ respectively are :