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A ball of mass 'm' moving horizontally at a speed 'v' collides with the bob of a simple pendulum at rest. The mass of the bob is also' 'm, if the collision is perfectly elastic, the bob of the pendulum will rise to a height of

A block of mass $100\text{gram}$ attached to a spring of stiffness $25\text{N/m}$ is lying on a frictionless floor as shown in figure. The block is moved to compress the spring by $8\text{cm}$ and released. If collision with the wall is elastic, find the time period of oscillations.

A satellite of the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly disappears, the satellite will

A force $F=5+2x+3x^2$ acts on a particle in $x$ direction where $F$ is in Newton and $x$ is in meter . Find the workdone by this force during a displacement from $x=1\text{m}$ to $x=2\text{m}$.

A tuning fork with a time period of $\frac{1}{256}\text{s}$ produces a sound wave in which the separation between adjacent compression and rarefaction is $0.7\text{m}$. Then, the speed of sound wave is

A radio transmitter radiates 1 kW power at a wavelength 198.6 metres. How many photons does it emit per second

A stone is dropped from the top of a tower of $500\text{m}$ height, into a pond of water at the base of the tower. When is the splash heard at the top?



$(\text{Given}g=10{\text{ms}}^{-2}$ and speed of sound $=340{\text{ms}}^{-1})$

What can be the unit vector of a plane to which a perpendicular dropped from origin(o) meet at A(1, 4, 6)?

In the system shown, mass of block A, B and C are $m_A=4m,m_B=3m$ and $m_C=8m$. If the system is released from rest, find the acceleration of block $B$. Assume all surfaces to be smooth and string inextensible.

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\text{sec}$ it rotates through an angle ${\theta }_1$, in the next $2\text{sec}$ it rotates through an additional angle ${\theta }_2$. The ratio of $\frac{{\theta }_2}{{\theta }_1}$ is

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is $p$ at a point where the velocity of flow is $v$, what is the pressure at another point where the velocity of flow is $2v,\rho$ being the density of water?

Which of these situations shown are in stable equilibrium?

How many grains of rice should the king give to satisfy the champion ?

In equation, $r=m^2\sin \left(\pi t\right)$, where $t$ represents time. If the unit of $m$ is $\text{N}$, then the unit of $r$ is

What is the dimension of density?

Three particles each of mass m, are situated at the vertices of an equilateral triangle of side length a. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation a. Find the initial velocity that should be given to each particle and also the time required for the circular motion

The potential energy function of a particle is given by $U=-(x^2+y^2+z^2)\text{J}$, where $x,y$ and $z$ are in meters. Find the force acting on the particle at point $A(1\text{m},3\text{m},5\text{m})$.

What is the equivalent resistance between the points A and B of the circuit shown in figure.

A steel ball strikes a steel plate at an angle $\theta$ with the vertical. If the coefficient of restitution is $e$, the angle at which the rebound will take place is

A vehicle, with a horn of frequency n, is moving with a velocity of 30 m/s in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency n + n₁. Then n₁ is equal to (take velocity of sound in air as 330 m/s)

A particle starts from rest at time $t=0$ and moves on a straight line with acceleration as plotted in figure. The speed of the a particle will be maximum at time

The seconds hand of a watch has length $6cm$. Speed of the end point and magnitude of difference in velocities at positions $A$ and $B$, as shown in the figure will be

If ${\mu }_s\text{and}{\mu }_k$ represent the coefficients of static and kinetic friction with appropriate suffixes for the two bodies shown, find the acceleration of the system. Take $g=10m/s^2$.

Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index $\mu$ is placed on face AC of the pr 9 is m. The prism is made of glass of refractive index $\frac{3}{2}$. The limits of $\mu$ for which total internal reflection takes place on face AC is

A spring of natural length $2x\text{m}$ is elongated such that its extension is twice its original length. If the force constant($k$) of spring is $8\text{N/m}$, the potential energy ($\text{J}$) stored in the spring is:

A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity of 30 m/s. The third piece has three times mass of each of the other piece. The magnitude and direction of the velocity of the third piece would be

What can the slope be in terms of theta?

Water drops falls from a tap at an interval of $2\text{second}$. Find out the position of $1^{st}$ drop when $6^{th}$ drop just leaves

A dipole consists of two particles one with charge $+1\mu C$ and mass $1\text{kg}$ and the other with charge $-1\mu C$ and mass $2\text{kg}$ separated by a distance of 3 m. For small oscillations about its equilibrium position, the angular frequency, when placed in a uniform electric field of $20\text{kV/m}$ is

A linear simple harmonic oscillation has a total energy of $250\text{J}$. If the potential energy at mean position is $50\text{J}$, then find the maximum kinetic energy.

A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following

A copper block of mass $2\text{kg}$ is heated to a temperature of ${500}^{\circ }\text{C}$ and then placed in a large block of ice at $0^{\circ }\text{C}$. What is the maximum amount of ice that can melt? The specific heat of copper is $400{\text{J kg}}^{-1}$ ${}^{\circ }{\text{C}}^{-1}$and latent heat of fusion of water is $3.5\times {10}^5{\text{J kg}}^{-1}$.

A pulse moving along $x-$axis is represented by the wave function $y(x,t)=\frac{2}{(x-2t{)}^2+1}$ where $x$ and $y$ measured in centimeters and $t$ is measured in seconds. The shape of pulse $y(x,0)=\frac{2}{x^2+1}$ is shown in the figure below. Which of the following correctly represents the shape of pulse at $t=1\text{s}$.

Four homogeneous brick, each of length $L=4\text{m}$, are arranged as shown in the figure. Each brick is displaced with respect to one in contact by $\frac{L}{8}.$ Find the $x-$ coordinate of centre of mass relative to origin $O$.

A ball is released from the top of tower of height $h$ meter. It takes $T$ second to reach the ground. What is the position in $\text{(m)}$ from the ground of the ball in $\frac{T}{3}$ second?

A ball of mass $m=0.5\text{kg}$ is attached to the end of a string having length $l=0.5\text{m}$. The ball is rotated on a horizontal circular path about the vertical axis, as shown in figure. The maximum tension that the string can bear is $324\text{N}$. Then, maximum possible value of angular speed of ball (in $\text{rad/s}$) will be:

A pendulum executes SHM. The acceleration of the bob of pendulum is ${\pi }^2{\text{m/s}}^2$ at a distance of $2\text{m}$ from the mean position. Find the time period of oscillation.

A particle of mass 'm' and charge 'q' is accelerated through a potential difference of 'V' volt. Its energy is

A ball is thrown upward from the edge of a cliff with an initial velocity of $8\text{m/s}$. How fast will it go at $0.5\text{sec}$ later.

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

Consider a system of two particles having masses $2\text{kg}$ and $4\text{kg}$. If the particle of mass $2\text{kg}$ is pushed towards the centre of mass of the particles through a distance $2\text{m}$, by what distance would the particle of mass $4\text{kg}$ move, so as to keep the centre of mass at the original position?

Two unequal forces are acting on a body. Can it ever be at rest, with respect to ground?

The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is

A solid cylinder of mass m = 4 kg and radius R = 10 cm has two ropes wrapped around it, one near each end. The cylinder is held horizontally by fixing the two free ends of the cords to the hooks on the ceiling such that both the cords are exactly vertical. The cylinder is released to fall under gravity. Find the tension in the cords when they unwind and the linear acceleration of the cylinder.

A particle is projected so as to graze the top of two walls each of height $20m$. The walls are at distances of $30m$ and $170m$ respectively from the point of projection. Find the angle of projection.

Two point charges placed at a distance ${}^{\prime }{r}^{\prime }$ in air exert a force ${}^{\prime }{F}^{\prime }$. The distance at which they exert same force when placed in a certain medium (dielectric constant $K$) is

A car when passes through a convex bridge exerts a force on it which is equal to

Three uniform bricks each of length $100\text{cm}$ and mass $m$ are arranged as shown in figure. The distance of centre of mass of the system of bricks from the wall is

An explosion blows a rock into three parts. Two pieces go off at right angles to each other; 1.0 kg piece with a velocity of 12 m/s and other 2.0 kg piece with a velocity 8 m/s. If the third piece flies off with a velocity 40 m/s, compute the mass of third piece.

Two bodies M and N of equal masses are suspended from two separate springs of the spring constant $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to that on N is