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A bullet is dropped from the same height when another bullet is fired horizontally. They will hit the ground

Two particles of masses $m$ and $2m$ moving in opposite direction collides elastically with velocities $2v$ and $v$ respectively. Find their respective magnitude of velocities after the collision.

Which of these options is the correct tangent to the given curve at the topmost point A

Five equal resistances each of resistance R are connected as shown in the figure. A battery of 4 volts is connected between A and B. The current flowing in AFCEB will be

When a plane mirror is placed horizontally on level ground at a distance of $60\text{m}$ from the foot of a tower, the top of the tower and its image in the mirror subtends an angle of ${90}^{\circ }$ at the corner of the mirror nearer to the foot of tower. The height of the tower is

In order to measure physical quantities in the sub-atomic world, the quantum theory often employs energy $E$, angular momentum $J$ and velocity $c$ as fundamental dimensions instead of the usual mass, length and time. Then, the dimension of force in this theory is

Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism. The angle of prism is $(cos{41}^{\circ }=0.75)$

A smooth sphere of mass $m$ is moving on a horizontal plane with velocity $3\hat{i}+\hat{j}$. It collides with a vertical wall which is parallel to vector$\hat{j}$. If the coefficient of restitution is $0.5$, the angle of velocity of the ball with repect to the normal to the wall after impact will be

A simple pendulum of length $l$ and bob mass m is displaced from its equilibrium position O to a position P so that the height of P above O is $h$ and is released. What is the tension in the string when the bob passes through the equilibrium position O? Neglect friction. V is the velocity of the bob at O

Two charges placed in air repel each other by a force of ${10}^{N}N.$ When oil is introduced between the charges, the force becomes $2.5\times {10}^{-5}N$. The dielectric constant of oil is

Two particles are projected from the ground simultaneously with speeds $20m/s$ and $\frac{20}{\sqrt{3}}m/s$at angles ${30}^{\circ }$ and ${60}^{\circ }$ with the horizontal in the same direction. The maximum distance between them till both of them strike the ground is approximately ($g$ = $10m/s^2$)

A tuning fork vibrates at $264\text{Hz}$. The shortest length of a closed organ pipe that will resonate with the tuning fork is

[Speed of sound in air $=350\text{m/s}$]

The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity $u$. If $l$ is the length of the pendulum, find the tension in the string when $\theta ={90}^{\circ }$ from the vertical. Given: $u=\sqrt{3gl}$

Consider a rain drop of mass $1\text{g}$ falling from a height of $2\text{km}$. It hits the ground with a speed of $50\text{m/s}$. The work done by resistive force of air is

$(g=10{\text{m/s}}^2)$

A block of mass $m$ is placed at rest on the top of a smooth wedge of mass $M$, which in turn is placed at rest on a smooth horizontal surface as shown in figure. Then the distance moved by the wedge as the block reaches the foot of the wedge is

The frequency of a car horn is 400 Hz. If the horn is honked as the car moves with a speed $u_s$ = 34 m/s through still air towards a stationary receiver, the wavelength of the sound passing the receiver is [velocity of sound is 340 m/s]

Find the average velocity of a projectile between the instants it crosses one third of the maximum height. It is projected with $u$ making an angle $\theta$ with the vertical.

A man standing on a road has to hold his umbrella at ${60}^o$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\sqrt{3}km/h$. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to the ground.

In Young's double slit experiment, if the two slits are illuminated with separate sources, no interference pattern is observed because

Find the acceleration of the $3m$ block when the system is released from rest. All other surfaces are smooth except between $m$ and $2m$. Take $g=10m/s^2$

In the figure shown below, two metallic slabs of same area of cross section and thickness having thermal conductivities $500{\text{W/m}}^{\circ }\text{C}$ and $600{\text{W/m}}^{\circ }\text{C}$ respectively are connected to the same temperature difference in parallel combination. Find the equivalent thermal conductivity (in ${\text{W/m}}^{\circ }\text{C}$)

Two seconds after projection a projectile is travelling in a direction inclined at ${30}^{\circ }$ to the horizontal after one more sec, it is travelling horizontally, the magnitude and direction of its velocity are

When the temperature of a rod increases from $T$ to $T+\Delta T$, the moment of inertia of the rod about an axis increases from $I$ to $I+\Delta I$. If the coefficient of linear expansion of rod is $\alpha$, then find the ratio $\frac{\Delta I}{I}$

A block of mass $m=15\text{kg}$ is attached to a spring of stiffness $K=100\text{N/m}$. The block descends a plane inclined at an angle $\alpha ={30}^{\circ }$ with horizontal. Assuming there is no friction, determine the acceleration of the block when the spring has stretched by a length $x=0.05\text{m}$.(Acceleration due to gravity is $10{\text{m/s}}^2$)

A ball is thrown vertically up from a tower of height $60\text{m}$ with a speed of $20\text{m/s}$. The $v-t$ curve of the ball is

[Take upward positive and $g=10{\text{m/s}}^2$]

Two very long straight parallel wires carry currents of same magnitude and in the same direction. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires, in the plane of the wires. Its instantaneous velocity $\overrightarrow{v}$ is perpendicular to this plane. The magnitude of the force due to magnetic field acting on the charge at this instant is

A particle of mass $2\text{kg}$ executes simple harmonic motion and its potential energy $U$ varies with position $x$ as shown below. The period of oscillation of the particle is

A motor cyclist moving with a velocity of $72\text{km/h}$ on a flat frictionless road takes a turn on the road at a point where the radius of curvature of the road is $20\text{m}$. The acceleration due to gravity is $10{\text{m/s}}^2$. In order to avoid skidding, he must bend with respect to the vertical plane by an angle

A man of mass $60\text{kg}$ is standing on a platform of mass $140\text{kg}$ kept on a smooth horizontal surface. The man starts moving on the platform with a velocity $2\text{m/s}$ relative to the platform. Find the recoil velocity of the platform.

Find the reading of the spring balance for the figure shown. Take $g=10m/s^2$

A beaker contains 200 gm of water. The heat capacity of the beaker is equal to that of 20 gm of water. The

initial temperature of water in the beaker is ${20}^{\circ }C.$ If 440 gm of hot water at ${92}^{\circ }C$ is poured in it, the final

temperature (neglecting radiation loss) will be nearest to

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with a constant angular acceleration $\alpha$. If the coefficient of static friction between the rod and bead is $\mu$, and gravity is neglected, then the time after which the bead starts slipping is:

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction $x_1\left(t\right)=Asin\omega t$ and $x_2\left(t\right)=Asin(\omega t+\frac{2\pi }{3})$. Adding a third sinusoidal displacement $x_3\left(t\right)=Bsin(\omega t+\varphi )$ brings the mass to a complete rest. The values of B and $\varphi$ are

A solid sphere is rolling on a surface as shown in the figure with a translational velocity $v$. If it is to climb the inclined surface, then $v$ should be

If the length of the rod $A$ is $(3.25\pm 0.01)\text{cm}$ and that of the rod $B$ is $(4.19\pm 0.01)\text{cm}$ then the rod $B$ is longer than rod $A$ by

A gaseous mixture enclosed in a vessel consists of one $\text{gram mole}$ of a gas $A$ with $\gamma =\frac{5}{3}$ and some amount of gas $B$ with $\gamma =\frac{7}{5}$ at a temperature $T$. The gases $A$ and $B$ do not react with each other and are assumed to be ideal. Find the number of moles of the gas $B$ if $\gamma$ for the gaseous mixture is $\left(\frac{19}{13}\right)$.

Two balls of masses $1\text{kg}$ and $2\text{kg}$ are moving with speeds $2\text{m/s}$ and $5\text{m/s}$ as shown in figure. Find the impulse of deformation of $2\text{kg}$ mass.

A small block of mass $m$ rests on a smooth wedge of angle $\theta$. With what horizontal acceleration $a$ should the wedge be pulled, as shown in the figure, so that the block falls freely.

A uniform metre stick of mass $250\text{gm}$ is suspended from the ceiling through two vertical strings of equal lengths. A small object of mass $50\text{gm}$ is placed on the stick at a distance of $70\text{cm}$ from the left end. Find the tension in both the strings. Take $g=10{\text{m/s}}^2$.