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A cricket ball of mass 150 gm is moving with a velocity of 12 m/s and is hit by a bat so that the ball is turned back with a velocity of 20 m/s. The force of blow acts for 0.01s on the ball. The average force exerted by the bat on the ball is

The density of an ideal gas is $6\times {10}^{-2}{\text{kg/m}}^3$ and the root mean square velocity of the gas molecules is $500\text{m/s}$. The pressure exerted by the gas on the walls of the vessel is

In figure shown, all surfaces are smooth. A force $F=2mg$ is acting on block $A$. If $R$ is contact force between $A$ and $B$ and $a$ is acceleration of $B$, then

A body of mass $m_1$ is moving with a velocity 'v'. It collides with another stationary body of mass $m_2$. They get embedded. At the point of collision, the velocity of the system is

What minimum amount of force is required to move a 10kg block kept on a horizontal surface. Given (${\mu }_s$=0.5), (${\mu }_k$=0.4) If the block was already moving then what would be the minimum force required to maintain its velocity at a constant value?

Dimensional representation of co-efficient of friction is

A body acted upon by a force of $50\text{N}$ is displaced through a distance $10\text{m}$ in a direction making an angle of ${60}^{\circ }$ with the force. The work done by the force is

(Take $W=\overrightarrow{F}.\overrightarrow{S}$, where $W$ is work done, $\overrightarrow{F}$ is force and $\overrightarrow{S}$ is the displacement)

Three particles $\text{A, B}$ & $\text{C}$ of masses $4m,2m$ & $3m$ are placed on the vertices of a equilateral triangle of length $2L$ as shown in the figure.



Find out the perpendicular distance of centre of mass from the side $\text{AB}$.

Okay I will give you another easy one. Just one last.

Find the angular momentum of the electron in $2^{nd}$ orbit of $H{e}^{+}$ ion.

Find the distance covered by a particle during the time interval $t=0$ to $t=20\text{s}$ for which the speed-time graph is shown in the figure.

An extended horizontal object $AB$ is placed in front of a plane mirror inclined at ${45}^{\circ }$ with horizontal as shown in the figure. The image of $AB$ in plane mirror will look like:

Two elastic rods are joined between fixed supports as shown in the figure. If there is no change in the lengths of the individual rods with increase in temperature, then choose the correct option.

[${\alpha }_1=2{\alpha }_2,Y_1=Y_2$ ($Y$ is Young's modulus, $\alpha$ is the linear expansion coefficient and $A$ is the cross-sectional area of rod)]

A marble of mass $x$ and diameter $2r$ is gently released in a tall cylinder containing honey. If the marble displaces mass $y(<x)$ of the liquid, then the terminal velocity is proportional to

The top of a lake gets frozen at a place where the surrounding air is at a temperature of $-{20}^{\circ }C$. Then choose the correct statement.

The mass $M$ of the hanging block in figure which will prevent the small block from slipping over the triangular block, if all the surfaces are frictionless and the strings and the pulleys are light is

At what temperature will the speed of sound in a monoatomic gas be the same as in a diatomic gas at ${127}^{\circ }\text{C}$? Molar mass of diatomic and monoatomic gases are in the ratio $16:1$.

A charge $q$ is placed at the centre of the line joining two equal charges $Q.$ The system of three charges will be in equilibrium, if $q$ is equal to

Trajectory of particle in a projectile motion is given as $y=x-\frac{x^2}{80}$. Here, $x$ and $y$ are in metre. For this projectile motion match the following and select proper option $(g=10{\text{m/s}}^2)$:

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& \text{Angle of projection}& \text{(p)}& 20\text{m}\\ \text{(B)}& \text{Angle of velocity}& \text{(q)}& 80\text{m}\\ & \text{with horizontal}& & \\ & \text{after}4s& & \\ \text{(C)}& \text{Maximum height}& \text{(r)}& {45}^{\circ }\\ \text{(D)}& \text{Horizontal range}& \text{(s)}& {\tan }^{-1}\left(\frac{1}{2}\right)\end{array}$

Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height $h_0$ and pressure $2P_0$ where $P_0$ is the atmospheric pressure. There is a hole in the wall of the tank at a depth $h_1$ below the top from which water comes out. A long vertical tube is connected as shown.





Find the height $h_2$ of the water in the long tube above the top initially.

A wave going in a solid

A glass flask of volume one litre at $0{}^{\circ }\text{C}$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100{}^{\circ }\text{C}$. Find the amount of mercury that will spill out, if the coefficient of volume expansion of mercury is $1.82\times {10}^{-4}{/}^{\circ }\text{C}$ and the coefficient of linear expansion of glass is $0.1\times {10}^{-4}{/}^{\circ }\text{C}$ respectively.

Block $B$ rests on a smooth surface. If the coefficient of static friction between $A$ and $B$ is $\mu =0.4$. Determine the acceleration of each block, if weight of lower block is $250N$ and $F=30N$.

A light string passing over a frictionless pulley has masses attached to its ends as shown in the figure. The tension in the thread will be

An object is at $2\text{m}$ at $t=0\text{sec}$. Its velocity is given by $v=2t+7$, its position at $t=5\text{sec}$ is

An object is placed symmetrically between two plane mirrors inclined at an angle of ${72}^{\circ }$, then the total number of images observed will be

At t = 0, the shape of a travelling pulse is given by $y(x,0)=\frac{4\times {10}^{-3}}{8-(x{)}^2}$ where x and y are in metres. The wave function for the travelling pulse if the velocity of propagation is 5 m/s in the +x direction is given by

On a winter day sound travels 336 meters in one second. Find the atmospheric temperature. Speed of sound at 0${}^{\circ }$ C = 332 m s${}^{-1}$.

The cathode of a photoelectric cell is changed such that the work function changes from $W_{1}to{W}_2(W_2>W_1)$. If the current before and after change are $l_{1}and{l}_2$ all other conditions remaining unchanged, then (assuming hn > $W_2$)

A block of mass $m$, lying on a horizontal plane is acted upon by a horizontal force $P$ and another force $Q$, inclined at an angle $\theta$ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is

(Assume $P>Q$)

In Young's double – slit experiment, the y – coordinates of central maxima and ${10}^{th}$ maxima are 2cm and 5cm, respectively. When the YDSE apparatus is immersed in a liquid of refractive index 1.5, the corresponding y – coordinates will be

The greatest height to which a man can throw a stone is h. The greatest distance to which he can throw it, will be

The rays of different colours fail to converage at a point after going through a converging lens. This defect is called

An electron and proton have the same de-Broglie wavelength. Then the kinetic energy of the electron is

A small bob is connected to one end of two identical massless strings each of length $12\text{cm}$. The other ends of the strings are fixed to a vertical rod as shown in the figure. If the tension in the first string $T_1$ is 2 times that of the tension in the second string $T_2$, then what will be the angular velocity of the bob?

A circular disc of radius ${}^{\prime }{r}^{\prime }$ and mass ${}^{\prime }{m}^{\prime }$ is rotating about an axis passing through its COM perpendicular to its plane with an angular speed $\omega$. If the radius of the disc is halved and the angular speed is doubled, which of the following options is correct?

A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to -$K/r^2$ , where K is a constant. The total energy of the particle is

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $(4t^3-2t)$, where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin

Photon of 5.5 eV energy fall on the surface of the metal emitting photoelectrons of maximum kinetic energy 4.0 eV. The stopping voltage required for these electrons are

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled $3m$ is

A stone is attached at the end of a string and rotated in a horizontal circle by a student. If the final speed of the stone is $2$ times the initial speed, then the final centripetal force is $x$ times the initial centripetal force. The value of $x$ is:

The $Si$ diode and the $Ge$ diode start conducting at $0.7\text{V}$ and $0.3\text{V}$ respectively, in the given circuit. If the $Ge$ diode connection be reversed. What will be the values of $V_0$ ​ and $I?$

Consider a car moving on a straight road with a speed of $100m{s}^{-1}$. The distance at which car can be stopped is $[{\mu }_k=0.5]$

The space between two plates $20\text{cm}\times 20\text{cm}\times 1\text{cm},1\text{cm}$ apart is filled with a liquid of viscosity $1\text{Poise}$. The upper plate is dragged to the right with a force of $F=5\text{N}$ keeping the lower plate stationary. The upper plate is moving at a constant speed $u$ as shown in figure.





What will be the velocity in $\text{m/s}$ of the flow at a point $0.5\text{cm}$ below the lower surface of the upper plate if linear velocity profile is assumed for the flow ?

The bob of simple pendulum having density $\frac{4000}{3}{\text{kg/m}}^3$ executes $\text{SHM}$ in water with a period ${}^{\prime }{t}^{\prime }\text{s}$. If the period of oscillation of bob in air is $10\text{s}$, find the value of ${}^{\prime }{t}^{\prime }$.

(Neglect frictional force of water, take density of water as $1000{\text{kg/m}}^3$)

Two rods of different materials, having coefficients of linear expansion ${\alpha }_1$ and ${\alpha }_2$ and Young's moduli $Y_1$ and $Y_2$ respectively, are fixed between two rigid walls. The rods are heated to the same temperature. There is no bending of the rods. If ${\alpha }_1:{\alpha }_2=2:3$, the thermal stress developed in the two rods will be equal provided $Y_1:Y_2$ is equal to