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A cantilever beam of span ${}^{\prime }{L}^{\prime }$ is loaded with a concentrated load ${}^{\prime }{P}^{\prime }$ at the free end. Deflection of the beam at the free end is

Which of the following graphs correctly represents a particle moving in a horizontal circle, if its magnitude of tangential acceleration is directly proportional to time and particle starts from rest?

The amount of charge passed in time t through a cross-section of a wire is Q(t) = At${}^2$ + Bt + C. (a) Write the dimensional formulae for A, B and C. (b) If the numerical values of A, B and C are 5, 3 and 1 respectively in SI units, find the value of the current, at t = 5 s.

A ball of mass $2\text{kg}$ is dropped from a height of $20\text{m}$. After striking the ground, the ball bounces back with half of its striking speed. Find the impulse imparted by the normal reaction from the ground. Take $g=10{\text{m/s}}^2$.

The space between the plates of a parallel plate capacitor of capacitance $9\mu \text{F}$ is filled with three dielectric slabs of identical size as shown in the figure. The new capacitance is

A single turn circular current carrying loop is placed in $xz$-plane with its centre at origin as shown. Area of loop is $5m^2$. Its magnetic dipole moment is



Diagrm

A candle of diameter d is floating on a liquid in a cylindrical container of diameter D(D >> d) as shown in figure. If it is burning at the rate of 2 cm/hour then the top of the candle will

The absolute temperature of air in a region linearly increases from $T_1$ to $T_2$ in a space of width d. Find the time taken by a sound wave to go through the region in terms of $T_1,T_2,d$ and the speed v of sound at 273 K.

A transverse harmonic wave on a string is described by

y(x,t) = 3.0 sin (36t + 0.018x + π/4)


Where x and y are in cm and t in s. The positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave?

If it is travelling, what are the speed and direction of its propagation?

(b) What are its amplitude and frequency?

(c) What is the initial phase at the origin?

(d) What is the least distance between two successive crests in the wave?

Two point charges $4\mu C$ and $1\mu C$ are placed $9m$ apart. A third point charge $q$ is placed on line joining $4\mu C$ and $1\mu C$. Value of $q$, so that all three charges can remain in equilibrium is

Two thin hoops of masses $m_1$ and $m_2$ have radii $r_1$ and $r_2$. They are mounted rigidly on a frame of negligible mass as shown. The moment of inertia of the system about an axis passing through the centre and perpendicular (normal ) to the frame is

Three charges $+Q$, $q$, $+Q$ are placed respectively, at distance, $0,\frac{d}{2}$ and $d$ from the origin, on the $x-$axis. If the net force experienced by $+Q$, placed at $x=0$, is zero, then the value of $q$ is:

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different height $a$ and $b$. The ratio of the time taken by the two to cover these distances are

Young's modulus of steel is $19\times {10}^{10}\frac{N}{m^2}$. Express it in $\frac{dyne}{c{m}^2}$. Here dyne is the CGS unit of force.

A voltage of peak value $283\text{V}$ and varying frequency is applied to a series $LCR$ combination in which $R=3\Omega ,L=25\text{mH}$ and $C=400\mu \text{F}$. Then, the frequency $\left(\text{in Hz}\right)$ of the source at which maximum power is dissipated in the above circuit, is

Air (ideal gas with $\gamma =1.4)$ at $1\text{bar}$ and $300\text{K}$ is compressed till the final volume is one-sixteenth of the original volume, following a polytropic process $P{V}^{1.25}=\text{const}.$

Calculate the (a) work done and (b) the energy transferred as heat per mole of the air.

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two non-zero vectors and$\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{B}\times \overrightarrow{A}$ then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

• What is radioactive decay?
• Spliting of heavy nucleus Ra with centre of mass at rest.why it is convenient to work with centre of mass rather than in laboratory frame of reference?(ncert)

In
the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of
thickness t is introduced in the path
of one of the interfering beams (wavelength l), the intensity at the
position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

[IIT-JEE (Screening) 2002]

An ideal Carnot engine having efficiency $\eta$ works between temperatures $127°C$ and $-73°C$. ${\eta }_1$ denotes the efficiency when the temperature of the source increases by $50°C$ and ${\eta }_2$ denotes efficiency when temperature of the sink decreases by $50°C$. Then the correct order is

Calculate the velocity of the centre of mass of the system of particles shown in figure.

Two resistance wires on joining in parallel the resultant resistance is 6/5 ohms. One of the wire breaks the effective resistance is 2 ohms. The resistance of the broken wire is

Answer: 2 ohm

A wire shown in the figure is moving with a velocity of $10\text{m/s}$ in the magnetic field of magnitude $0.3\text{T}$. If the distance between the points $\text{A}$ and $\text{B}$ is $15\text{cm}$. Calculate the emf induced between points $\text{A}$ and $\text{B}$.

A clock has a continuously moving second's hand of $0.1\text{m}$ length. The average accelaration of the tip of the hand (in units of ${\text{ms}}^{-2}$) is of the order of :

A thread is wound around two discs on either sides. The pulley and the two discs have the same mass and radius. There is no slipping at the pulley and no friction at the hinge. The linear acceleration of disc $1$, disc $2$ and the angular acceleration of pulley be $a_1$, $a_2$ and $\alpha$ respectively. Then

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to

1. 63.04

1. 31.41

The proportional limit of steel is $8\times {10}^8{\text{N/m}}^2$ and its young modulus is $2\times {10}^{11}{\text{N/m}}^2.$ The maximum elongation, a one meter long steel wire can be given without exceeding the proportional limit is

When an ideal monoatomic gas is heated at constant pressure, the fraction of heat energy supplied which increases the internal energy of gas is

300 cm^{2} =