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The velocity of a freely falling body one second after being dropped is

The displacement $x$ of a simple harmonic oscillator varies with time $t$ as

$x\left(t\right)=0.5\sin (2\pi t+\frac{\pi }{4})$

What is the magnitude of maximum acceleration ?

The speed of a boat in still water is $\sqrt{5}\text{m/s}$ . While crossing a river, the average speed of the boat is $3\text{m/s}$. If boat crosses the river in the shortest possible time, what is the speed of flow of water?

Evaluate $\int \frac{6}{-3x+6}dx$

A capacitor of capacitance, $C=25\mu \text{F}$ is fully charged and then connected with an inductor of inductance, $L=10\text{mH}$. The ratio of magnitude of maximum charge on the capacitor to the maximum current through the circuit, is -



Assume ideal conditions.

A vessel contains 1.60 g of oxygen and 2.80 g of nitrogen. The temperature is maintained at 300 K and the volume of the vessel is 0.166 $m^3$. Find the pressure of the mixture.

Figure shows an overhead view of a corridor with a plane mirror M mounted at one end. A burglar B sneaks along the corridor directly toward the center of the mirror. If d = 3.0 m, how far from the mirror will she be when the security guard S first sees her in the mirror?

An electromagnetic wave of frequency, $1\times {10}^4\text{Hz}$ is propagating along $z-$axis. The maximum amplitude of the electric field is $4\text{V/m}$. Average energy density of the electric field will be -

What is the rest mass energy of an electron?

Six particles situated at the corners of a regular hexagon of side 'a' move at a constant speed 'v'. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.

A particle of mass $1\text{g}$ executes an oscillatory motion on the concave surface of a spherical dish of radius $2\text{m}$ placed on a horizontal plane. If the motion of the particle begins from a point on the dish at a height of $1\text{cm}$ from the horizontal plane and the coefficient of friction is $0.01$, the total distance covered by the particle before it comes to rest, is approximately

A spring of negligible mass having a force constant k extends by an amount y when a mass m is hung from it. The mass is pulled down a little and released. The system begins to execute simple harmonic motion of amplitude A and angular frequency $\omega$. The total energy of the mass - spring system will be

A $1kg$ body falls vertically with a speed of $25m/s$ and rebounds with a speed of $10m/s$. If the time for which the ball is in contact with the ground is $1ms$, what is the contact force on the body by the ground?

Calculate the compressibility factor for a gas, if $1$ mole of it occupy $0.821\text{litre}$ at $300\text{K}$ and $50\text{atm}$.

The flux entering and leaving a closed surface are 5×10^5 and 4×10^5 in si unit the charge inside the surface is

-8.85×10^-7 c

8.85×10^-7

8.85×10^-7

-6.85×10^7

6.85×10^-7

Two short electric dipoles of moment $P$ and $27P$ are placed as shown below. If at the point $O$ the electric field is zero between the dipoles, then the distance of the point $O$ from the centre of first dipole is

A cyclic process for $1$ mole of an ideal gas is shown in figure in the $V-T$ diagram. The work done in process $AB,BC$ and $CA$ respectively, are

A rock band gives rise to an average sound level of $100\text{dB}$ at a distance $20\text{m}$ from the centre of the band. As an approximation, assume that the sound radiated by the band spreads out in the shape of a sphere centred at the band. What is the power of sound produced by the band?

In the experimental setup of metre bridge shown in the figure, the null point is obtained at a distance of $40\text{cm}$ from $\text{A}$. If a $10\Omega$ resistor is connected in series with $R_1\Omega$ , the null point is observed to shift by $10\text{cm}$ from $\text{A}$. Find the resistance that should be connected in parallel with $(R_1+10)$$\Omega$ such that the null point shifts back to its initial position is

A convex lens forms a real image three times larger than the size object on a screen. Object and screen are moved until the image becomes twice the size of the object. If the shift of the object is $6\text{cm}$ (away from the lens), the shift of screen is :

The coefficients of static and kinetic friction between a body and the surface are 0.75 and 0.5 respectively. A force is applied to the body to make it just slide with a constant acceleration which is equal to

The differential entropy of a Gaussian random variable with zero mean and variance of 2 will be

What happens to the centripetal acceleration of a revolving body if you double the orbital speed v and half the angular velocity $\omega$

A uniform bar of length $6\text{m}$ and mass $16\text{kg}$ lies on a smooth horizontal table. Two point masses $2\text{kg}$ and $4\text{kg}$ moving in the square horizontal plane with $6\text{m/s}$ and $3\text{m/s}$ respectively strike the bar as shown in figure and stick to the bar after collision. Denote angular velocity (about the centre of mass), total energy and centre of mass velocity by $\omega ,E$ and $v_c$ respectively. Then after the collision:

A set of $n$ equal resistors of value $R$ each are connected in series to a battery of emf $E$ and internal resistance $R$. The current drawn is $I$. Now, the $n$ resistors are connected in parallel to the same battery. Then the current drawn from battery becomes $10I$. The value of $n$ is

A point moves in x-y plane according to the law x=4 sin 6t and y=4(1-cos 6t). The distance traversed by the particle in 4 seconds is (x and y are in meters)

A periodic voltage wave form has been shown in the figure. Determine the frequency of the wave form.

Figure illustrates a cycle conducted with $n$ moles of an ideal gas. In the states $a$ and $b$ the gas temperatures are $T_a$ and $T_b$ respectively. Temperature of the gas in the state $c$ is

Find equivalent resistance of the circuit.

A particle of mass $m$ is moving with constant velocity $v$ parallel to $x$-axis in $x-y$ plane as shown in figure. Calculate its angular momentum with respect to origin at anyinstant '$t$'.

The displacement of particle in a periodic motion is given by $y=4{\text{cos}}^2\left(\frac{t}{2}\right)\text{sin}1000t$. This displacement may be considered as the result superposition of $n$ independent harmonic oscillations. Here the value of $n$ is :