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According to Gauss' Theorem, electric field of an infinitely long straight wire is proportional to

A wave travels on a light string. The equation of the wave is $y=Asin(kx+wt+{30}^{\circ }+{180}^{\circ })$, it is reflected from a heavy string tied to an end of the light string at x= 0. If 64% of the incident energy is reflected then what is the equation of the reflected wave?

A hockey player applies an average force of $60\text{N}$ to $250\text{g}$ hockey puck for a time of $100\text{ms}$. The impulse experienced by the hockey puck is

A police jeep is chasing with, velocity of $45\frac{km}{h}$ a thief in another jeep moving with velocity $153\frac{km}{h}$. Police fires a bullet with muzzle velocity of $180\frac{m}{s}$. The velocity it will strike the car of the thief is

Find the acceleration of the two bodies if the system is shown, is initially at rest. Take $g=10{\text{m/s}}^2$.

A stone is projected from the ground with velocity $50m{s}^{-1}$ and angle of ${30}^{\circ }$. It crosses a wall after $3s$. How far beyond the wall the stone will strike the ground?

Take $g=10m{s}^{-2}$

A particle p is moving in a circle of radius 'd' with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio

A composite string is made by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. A transverse wave pulse. $y=\left(6\text{mm}\right)\sin (5t+40x)$, where '$t$' is in seconds and '$x$' is in meters, is sent along the lighter string towards the joint. The joint is at $x=0$. The equation of the wave pulse reflected from the joint is $y=\left(2\text{mm}\right)\sin (5t-40x+\pi )$. The percentage of the power transmitted to the heavier string through the joint is approximately

Boat A is sailing towards north-east with velocity $\overrightarrow{v}=5\hat{i}+5\hat{j}km/hr$, where $\hat{i}$ points east and $\hat{j}$, north. Boat B is at a distance of $50km$ east and $100km$ north of boat A and is sailing towards west at $10km/hr$. A will be at minimum distance from B in:

Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 200${}^{\circ }$C. During the day the temperature rises to 400${}^{\circ }$C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature

The equation of progressive wave in a wire is given by $y=0.15sin\left[2\pi (15t-\frac{x}{10})\right]$

Where the distance is in meters and time in seconds.

Determine i) amplitude, ii) frequency, iii) wavelength and iv) velocity of the wave

A solid cylinder is released from rest from the top of an inclined plane of inclination $\theta$ and length ${}^{\prime }{l}^{\prime }$. If the cylinder rolls without slipping, then find it's speed when it reaches the bottom of inclined plane.

The graph of displacement v/s time is





Its corresponding velocity-time graph will be

A ball initially at rest falls from a height $h=2.5\text{m}$. After collision with surface having value of coefficient of restitution $e=0.6$, it rebounds back. Find the rebound velocity of ball.

In a satellite if the time of revolution is T, then kinetic energy is proportional to

Will a man in a lift in space accelerating up with an acceleration g feel any different from a man in a stationary lift on Earth?

The position of a particle moving in a straight line is described by the relation $x=6+12t-2t^2\text{m}$. The distance covered by the particle in first $5\text{s}$ is

A uniform solid brass sphere is rotating with angular speed ${\omega }_0$ about a diameter. If its temperature is now increased by ${100}^{\circ }\text{C}$. What will be its new angular speed? (Given ${\alpha }_B=2.0\times {10}^{-5}{\text{per}}^{\circ }C$)

For an object moving with a speed $v$ in front of a plane mirror as shown in the figure, identify the correct diagram representing motion of its image with respect to ground.

Consider the situation as shown in figure. A plane mirror is fixed at a height $h$ above the bottom of a beaker containing water (refractive index $\mu$ ) up to a height $d$. Find the position of the image of the bottom formed by the mirror.

The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the magnitudes of forces?

Figure shows a stream of water emerging from the opening of a tap. As the water falls through a height $h=PQ$, the cross-sectional area of the stream decreases from $A$ to $a$. Obtain the expression for the rate of flow of water through the opening of the tap.

For adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to :

Two successive resonance frequencies in an open organ pipe are 1944 Hz and 2592 Hz. Find the length of the tube. The speed of sound in air is $324m{s}^{-1}$

A wire has resistance $12\Omega$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to

Work done for the process A$\to$ B shown in the figure is

A particle is moving in a circle of radius $R$ in such a way that at any instant, the radial and tangential components of acceleration are equal. If its speed at $t=0$ is $v_0$, the time taken to complete the first two revolutions is:

A solid cylinder is rolling without sliding. What fraction of its total kinetic energy is associated to rotational motion ?

A particle tied to a string describes a vertical circular motion of radius $R$ continuously. If it has velocity $\sqrt{3gR}$ at the highest point, then the ratio of respective tensions in the string at the highest and lowest point is

The maximum range of a projectile is $48\text{m}$. When it is thrown at an angle of ${15}^{\circ }$ with the horizontal, its range will be-

A solid sphere of radius R and density $\rho$ is attached to one end of a massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density $3\rho$. The complete arrangement is placed in a liquid of density $2\rho$ and is allowed to reach equilibrium. The correct statement(s) is (are)

Seven capacitors each of capacitance $2\mu F$ are connected in a configuration to obtain an effective capacitance $\frac{10}{11}\mu F$. Which of the following combination will achieve the desired result?

A bullet of mass $50\text{gm}$ is fired from a gun towards a ball of mass $450\text{gm}$





The bullet hits the ball with speed $200\text{m/s}$ in horizontal direction as shown in figure, and remains inside it. Find the magnitude of velocity of system of (ball+ bullet) after collision.

The temperature at which the reading of Fahrenheit thermometer will be double that of a centigrade thermometer is

While calculating the focal length of a lens formula; what is different when the lens is immersed in or surrounded by some other medium than that of air?

A body of mass $2\text{kg}$ is thrown vertically up with kinetic energy of $500\text{J}$. What will be height at which the kinetic energy of the body becomes ${\frac{2}{3}}^{rd}$ of original value? $(g=10{\text{m/s}}^2)$

Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle ${}^{\prime }{\theta }^{\prime }$ with the vertical. If wires have mass $\lambda$ per unit length then the value of $I$ is

($g$ = gravitational acceleration)

A ray of light is incident at angle $i$ on a surface of a prism of small angle $A$ & emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$, the angle of incidence $i$ is nearly equal to

A box P and a coil Q are connected in series with an ac source of variable frequency. The emf of the source is constant at $10\text{V}$. Box P contains a capacitance of $1\mu F$ in series with a resistance of $32\Omega$. Coil Q has a self inductance of 4.9 mH and a resistance of $68\Omega$ in series. The frequency is adjusted so that maximum current flows in P and Q.



The voltage across Q is

In a double slit experiment when light of wavelength $400nm$ was used the angular width of the first minima formed on a screen placed $1m$ away was found to be $0.2°$. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? (${\mu }_{water}$ = 4/3)

A system of particles is shown in figure. Point mass particles of same mass $m$ are present at each corner of the hexagon whose each side is equal to $a$. Find the $MOI$ about an axis passing through its $COM$ and perpendicular to its plane.

A smooth chain $AB$ of mass $m$ rests against a surface in the form of a quarter of a circle of radius $R$. If it is released from rest, the velocity of the chain after it comes over the horizontal part of the surface is

The fundamental frequency of an open organ pipe is equal to the second overtone of a closed organ pipe. If the length of closed organ pipe is $40\text{cm}$, the length of open organ pipe is

A particle is moving along $x-$axis. Its $x-$coordinate versus time graph is shown.





Its $v-t$ graph will be:

A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is