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The area of cross-section of the two arms of a hydraulic press is $1{\text{cm}}^2$ and $20{\text{cm}}^2$, respectively. A force of $10\text{N}$ is applied on the water, on the liquid in the thinner arm. What force should be applied on the water in the thicker arm, so that the water levels may remain in equilibrium, in both arms?

Calculate the thermal efficiency of a Carnot's heat engine working between ice point and steam point.

A motor boat going down stream overcomes a float at a point A. 60 minutes later it turns and after some time passes the float at a distance of 12 km from the point A. The velocity of the stream is (assuming constant velocity for the boat in still water)

In a lab experiment, three capacitors each of capacitance $C$ and of breakdown voltage $V$ are joined in series. Then capacitance and breakdown voltage of the combination will be?

Two masses $A$ and $B$ of $5\text{kg}$ and $6\text{kg}$ are connected by a string passing over a frictionless pulley fixed at the corner of table as shown in figure. The coefficient of friction between $A$ and the table is $0.3$. The minimum mass of $C$ that must be placed on $A$ to prevent it from moving is equal to: $(\text{Take}=10{\text{m/s}}^2)$

Two squares of size $(a\times a)$ each are removed from a bigger square of size $(2a\times 2a)$ as shown in the figure. Removed parts are unshaded in the figure given below. Find the coordinates of the $COM$ w.r.t the origin $\text{O}$.

If Agl follows ZnS (zinc blended structure). If $I^{-}$ is at all lattice points then fraction of total voids that are occupied by $A{g}^{+}$.

A block of mass M is pulled along a horizontal surface by applying a force at an angle with the horizontal. The friction coefficient between the block and the surface is $\mu$. If the block travels at a uniform velocity, then the work done by this applied force during a displacement d of the block is—

A $p$-type semiconductor has acceptor level $57\text{meV}$ above the valence band. Find the maximum wavelength of light which can create a hole.

The energy associated with electric field is $\text{(}{U}_E)$ and with magnetic fields is $\left(U_B\right)$ for an electromagnetic wave in free space. Then

A transverse wave is described by the equation $Y=Y_{o}sin2\pi ⟮ft-\frac{x}{\lambda }⟯$. The maximum particle velocity is four times the wave velocity if

[IIT 1984; MP PMT 1997; EAMCET; 1998;CBSE PMT 2000; AFMC 2000; MP PMT/PET 1998; 01;KCET 1999, 04; Pb. PET 2001; DPMT 2005]

A body is sliding down a rough inclined plane of angle of inclination $\theta$ for which coefficient of friction varies with distance $y$ as $\mu \left(y\right)=Ky$, where $K$ is constant. Here $y$ is the distance moved by the body down the plane. The net force on the body is zero at $y=A$. Find the value of constant $K$.

A charge $-q$ is placed at the axis of a charged ring of radius $r$ at a distance of $2\sqrt{2}r$ as shown in the figure. If the ring is fixed and carrying a charge $+Q$, the kinetic energy of charge $-q$ when it is released and reaches the centre of the ring will be

Find the electric field vector at P(a,a,a) due to three infinitely long lines of charges along the x, y and z axis, respectively. The charge density i.e. charge per unit length of each wire is $\mathrm{\lambda .}$

The P.E. of a certain spring when stretched from its natural length through a distance 0.3 m is10 J. The amount of work in joule that must be done on this spring to stretch it through an additional distance 0.15 m will be

A ball is thrown vertically upwards with a speed of $9.8\text{m/s}$ from the top of tower. If it returns to ground in $3\text{seconds}$, find the height of tower. (Take $g=9.8{\text{m/s}}^2$)

A calorie is a unit of heat or energy and it equals about 4.2 J
where 1J = 1 kg m²s^–2. Suppose we employ
a system of units in which the unit of mass equals α kg, the
unit of length equals β m, the unit of time is γ
s. Show that a calorie has a magnitude 4.2 α^–1
β^–2 γ²
in terms of the new units.

A fire hydrant delivers water of density ρ at a volume rate l. The water travels vertically upwards through the hydrant and then does 90⁰ turn to emerge horizontally at speed υ. The pipe and nozzle have uniform cross-section throughout. The force exerted by water on the corner of the hydrant is

The density of a linear rod of length $L$ varies as $\rho =A+Bx$ where $x$ is the distance from the left end. Its centre of mass is at a distance (from the left end) of

Write Einstein's photoelectric equation and point out any two characteristic properties of photons on which this equation is based.
Briefly explain the three observed features which can be explained by this equation.

The pressure of water at the bottom of a water tank exceeds the atmospheric pressure by 10⁴ Pascal. The velocity of efflux of water through an orifice at the bottom of the water tank will be (g = 10 ms^-2).

The K.E of mole of an ideal gas is $E=\frac{3}{2}\text{RT}$. Then $C_p$ will be

A car is moving from A to B in straight line at constant acceleration. If velocities at A and B are u and v respectively, then velocity at the midpoint of A and B is

From a building two balls A and B are thrown such that A is thrown upwards and B downwards, both vertically and same magnitude. If $V_A$ and $V_B$ are their respective velocities on reaching the ground, then

An inductive coil has a resistance of $100\Omega ,$ when an $\text{a.c.}$ signal of frequency $1\text{kHz}$ is fed to the coil, the applied voltage leads the current by ${45}^{\circ }.$ What is the approximate inductance of the coil ?

A particle of mass $m$ carrying charge $q$ is accelerated by a potential difference $V$. It enters perpendicularly in a region of uniform magnetic field $B$ and executes a circular arc of radius $R$, then $\frac{q}{m}$ equals

If Sameer moves from point $A$ having position vector $2\hat{i}+4\hat{j}+2\hat{k}$ to point $B$ having position vector $6\hat{i}+8\hat{j}+3\hat{k}$, what is his displacement vector?

If the system shown in the figure is at rest initially, find the common acceleration of the two block system?

(Take $g=10m/s^2$)

Consider the system given below, The matrix A of the system in state model when controllable canonical form is used is $\frac{Y\left(s\right)}{U\left(s\right)}=\frac{5}{s^3+6s+7}$

Discuss mation of an object under free fall. Neglect air resistence.

An insect is crawling up a hemispherical bowl of radius R. If the coefficient of friction is $\frac{1}{3}$, what will be height h to which the insect will be able to crawl? Take $(\frac{3}{\sqrt{10}}=0.95)$

A $2kg$ object is subjected to three forces that give it an acceleration $\overrightarrow{a}=-8m/s^2\hat{i}$. If two of the three forces are $F_1=\left(30.0N\right)\hat{i}+16.0N)\hat{j}$ and $F_2=-\left(12N\right)\hat{i}+\left(8N\right)\hat{j}$, find the third force.

1. 0.826

One mole of ideal gas follows a law according to that it's pressure varies with volume as p= $\frac{a}{1+\frac{v}{b}}$where a and b are positive constant the temperature of the gas at volume v= a is

A wooden block of mass M rests on a horizontal surface. A bullet of mass m moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance x on the surface. If the coefficient of friction between wood and the surface is $\mu$, the speed of the bullet at the time of striking the block is (where m is mass of the bullet)