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A projectile is fired horizontally with a velocity of $98\text{m/s}$ from the top of a hill $490\text{m}$ high. Find the time taken by the projectile to reach the ground.

A sphere of mass $M=2\text{kg}$ moving with a velocity of $2\sqrt{2}\text{m/s}$ collides with another sphere of mass $m=1\text{kg}$ initially at rest at an angle of ${45}^{\circ }$ with the horizontal. If the coefficient of restitution of the collision is 0.5, what will be the final velocity(in $\text{m/s}$) of the sphere having mass $m$ ?

A water tank standing on the floor has two small holes punched in the vertical wall, one above the other. The holes are $2.4\text{cm}$ and $7.6\text{cm}$ above the floor. If the jets of water from the holes hit the floor at the same point, then the height of water in the tank is

There is a chain of length $6\text{m}$ and coefficient of friction $\frac{1}{2}$. What will be the maximum length of chain which can be held outside the table without sliding?

A tube of length $1\text{m}$ containing $H_2$ is closed at one end. If the velocity of sound in air be $340\text{m/s}$. Then, the fundamental frequency and the next higher overtone in $H_2$ are:

In a certain region uniform electric field $\overrightarrow{E}$ and uniform magnetic field $\overrightarrow{B}$ are present in opposite directions. A particle of mass $m$ and of charge $q$ enters in this region with a velocity $v$ at an angle $\theta$ from the magnetic field. The time after which the speed of the particle would be minimum is equal to :

Two bodies move toward each other from 10 m apart with a constant velocity they meet at C after 2s. What is the relative velocity of B w.r.t. A?

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $S$ is the area of cross section of the wire, the stress in the wire at a height $3L/5$ from its lower end is

If the temperature of a uniform steel rod of mass $12\text{kg}$ and length $1\text{m}$ is increased by $20{}^{\circ }\text{C}$, its moment of inertia about its perpendicular bisector increases by -
$[\alpha =11\times {10}^{-6}/{}^{\circ }\text{C}]$

A body, acted upon by a force of $100N$ is displaced through a distance $50$ meter in a direction making an angle of ${90}^{\circ }$ with the force. The work done by the force be

definiton of wave

Find electric potential at origin when all negative charges magnitude +Q are placed at 1, 1/3, 1/5, 1/7.. And -Q placed at 1/2, 1/4, 1/6.. Along x-axis.

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A body of weight 100 N is suspended with the help of strings as shown in figure. The tensions T₁ and T₂ will be

Two tuning forks of frequencies 256 and 258 vibrations/sec are sounded together, then time interval between consecutive maxima heard by the observer is

A bullet of $5$ g is fired from a pistol of $1.5$ kg. If the recoil velocity of pistol is $1.5$ $\frac{m}{s}$, find the velocity of bullet. (in $\frac{m}{s}$)

A motor boat is travelling with a speed of 3.0 m/sec. If the force on it due to water flow is 500 N, the power of the boat is

The angular velocity of a particle rotating in a circular orbit 100 times per minute is

A small particle of mass m is projected at an angle $\theta$ with the x-axis with an initial velocity $v_0$ in the x-y plane as shown in the figure. At a time $t<\left(v_{0}sin\theta /g\right),$ the angular momentum of the particle is

A block $\left(B\right)$ is attached to two unstretched springs $S_1$ and $S_2$ with spring constant $2k$ and $4k$ respectively. The other ends are attached to two supports $m_1$ and $m_2$ not attached to the walls. The springs and supports have negligible mass and the surface is frictionless. The block $B$ is displaced towards wall $1$ by a small distance $x$ and released. The block returns and moves a maximum distance $y$ towards wall $2$. Displacement $x$ and $y$ is measured with respect to the equilibrium position of the block $B$. The ratio of $\frac{y}{x}$ is

The resistance of a wire at ${20}^{\circ }C$ is $20\Omega$ and at ${500}^{\circ }C$ is $60\Omega$. At which temperature resistance will be $25\Omega$?

Sound signal is sent through a composite tube as shown in the figure. The radius of the semicircle is $r$. Speed of sound in air is $v$. The source of sound is capable to generate frequencies in the range $f_{1}to{f}_2(f_2>f_1)$. If $n$ is an integer then, frequency for maximum intensity is given by

A particle is fired vertically upward with a speed of 15 km $s^{-1}$ With what speed will it move in intersteller space. Assume only earth's gravitational field.

A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density $6g{m}^{-1}$ kept under a tension of 60 N. (a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 2.0 m long portion of the string.

A circular plate of uniform thickness has a diameter of $28\text{cm}$. A circular portion of diameter $21\text{cm}$ is removed from the plate as shown. $O$ is the centre of mass of complete plate. The position of centre of mass of remaining portion will shift towards left from $O$ by

Wires 1 and 2 carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire1

Angular momentum of a planet of mass m orbiting around sun is J, areal velocity of its radius vector will be

A block of mass $4\text{kg}$ is kept on a rough horizontal surface with coefficient of friction ${\mu }_s=0.4$ and ${\mu }_k=0.3$ and a time varying horizontal force $F=4t$ is applied on it. Then the acceleration - time graph of the particle is $(g=10{\text{m/s}}^2)$

The radius of curvature of the path of the charged particle in a uniform magnetic field is directly proportional to

[MNR 1995; UPSEAT 1999, 2000]

A bird flies for 4 s with a velocity of $|t-2|$ m/s in a straight line, where t is time in seconds. It covers a distance of

If vectors $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ have magnitudes $5,12$ and $13$ units and $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C},$ then the angle between $\overrightarrow{B}$ and $\overrightarrow{C}$ is

A car has an initial velocity of $60\text{m/s}$. On application of brakes the car stops after $300\text{m}$. The retardation (deceleration) of the car is

If the wavelength of the first line of the Balmer series in the hydrogen spectrum is $\lambda$, then the wavelength of the first line of the Lyman series is

A transverse periodic wave on a string with a linear mass density of 0.200 kg/m is described by the following equation where x and y are in metres and t is in seconds.

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX’ which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX’ axis is :

If the momentum of an electron is changed by P, then the de-Broglie wavelength associated with it changes by 0.5%. The initial momentum of electron will be:

A resistance ‘R‘ draws power ‘P‘ when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes ‘Z‘, the power drawn will be :

There are two mass less spring A and B of spring constant $K_A$ and $K_B$ respectively $K_A>K_B$ . If $W_{A}and{W}_B$ be denoted as work done on A andwork done on B respectively, then

If $S=e^x-\sin x$, find $\frac{d^{2}S}{d{x}^2}$

The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$ is given by