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A wedge of mass $M$ has one face making an angle $\alpha$ with horizontal and is resting on a smooth rigid floor. A particle of mass ${}^{\prime }{m}^{\prime }$ hits the inclined face of the wedge with horizontal velocity $v_0.$ It is observed that the particle rebounds in vertical direction after impact. Calculate the speed of particle after impact.

[Neglect friction between particle and the wedge and take $M=2m,v_0=10\text{m/s},\tan \alpha =2,g=10{\text{m/s}}^2.$]

A manometer connected to a closed tap reads $3.5\times {10}^5{\text{N/m}}^2$. When the valve is opened, the reading of the manometer falls to $3.0\times {10}^5{\text{N/m}}^2$. Then, the velocity of flow of water is:-

A constant force $10\text{N}$ acts on a ball of mass $2\text{kg}$ for $2\text{s}$ . Then another force $18\text{N}$ acts on the same ball for $\frac{10}{9}\text{second}$. If ball is initially at rest, then find the total work done.

If the momentum of a body increases by 0.01%, its kinetic energy will increase by

A string of length $L$ vibrates with a frequency of $7.5\text{Hz}$ to form a standing wave with three antinodes as shown below.


What is the oscillating frequency of this string, if it produces the standing wave pattern shown below?

In order to raise a mass of 100 kg, a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with acceleration 5 $\frac{g}{4}$ relative to the rope. The tension in the rope is (take g = 10 $m{s}^{-2}$)

Which of the following expression is true for surface tension?

Three charges $4\mu \text{C}$ each are kept at the vertices of an equilateral triangle of side $9\text{cm}$. The magnitude of force on one of the charges is

In figure, the block moves downwards with velocity $u_1$, the wedge moves rightwards with velocity $u_2$. The correct relation between $u_1$ and $u_2$ is

Two spherical balls $A$ and $B$ are connected by the massless rod. The masses of ball $A$ and $B$ are $2\text{kg}$ and $5\text{kg}$. Find the moment of inertia of the system about the axis passing perpendicular to the length of rod as shown in figure bellow.

The equivalent resistance between points $A$ and $B$ is:

An ideal liquid flowing through a pipe $\text{A}$ of cross-section $0.2{\text{m}}^2$ with velocity $10\text{m/s}$ enters a $\text{T}$ - junction. One side of the $\text{T}$ -junction $\text{B}$ has cross-section area $0.1{\text{m}}^2$ and the other side $\text{C}$ has cross-section area $0.05{\text{m}}^2$. If the velocity of water in $\text{C}$ is $15\text{m/s},$ then in $\text{B}$ the velocity is

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, first part of mass $1\text{kg}$ moving with a velocity of $12{\text{ms}}^{-1}$ and $2\text{kg}$ second part moving with a velocity of $8{\text{ms}}^{-1}.$ If the third part moves with $4{\text{ms}}^{-1},$ its mass would be

A point dipole $\overrightarrow{p}=-p_0\hat{x}$ kept at the origin. The potential and electric field due to this dipole on the $y-$axis at a distance $d$ are, respectively :

(Take $V=0$ at infinity)

A monochromatic light of $\lambda =6000\mathring{\text{A}}$ is incident on the slits. The interference pattern is observed on a screen and central maxima is formed at point $O$. A thin glass plate of thickness $0.4\mu \text{m}$ and refractive index $1.5$ is placed in front of one of the slits. If the intensity at point $O$ is $I_0$ initially, what will be the intensity at $O$ after placing the glass plate?

A thermodynamic system undergoes a cyclic process as shown in the figure. The cycle consists of two closed loops. Over one complete cycle, the system performs

A body of mass $m$ moving with a velocity $v$ in the x-direction collides with a body of mass $M$ moving with a velocity $V$ in the y-direction. They stick together during the collision. Choose the correct statement/statements.

A body is traveling in a straight line. It moves AB that is 5 m towards the east, BC that is 4 m towards north-east while making 30^o with north and CD that is 7 m in the west direction. Calculate the resultant displacement. [2 MARKS]

Find $\overrightarrow{A}\times \overrightarrow{B}$, if $\overrightarrow{A}=\hat{i}+2\hat{j}-4\hat{k}$ and $\overrightarrow{B}=2\hat{i}-\hat{j}+2\hat{k}$.

During the mean life of a radioactive element, the fraction that disintegrates is-

A charged particle moves in a uniform magnetic field perpendicular to it, with a radius of curvature $4cm$. On passing through a metallic sheet, it loses half of its kinetic energy. Then, the radius of curvature of the particle is

An electron moves along the line PQ which lies in the same plane as a circular loop of conducting wire, as shown in Fig. 25.5. What will be the direction of the induced current, if any, in the loop ?

Which set of quantum numbers is possible for the last electron of Mg⁺ ion?

On the $x-$axis at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by $\frac{Ax}{(x^2+a^2{)}^{3/2}}$ in the $x-$direction. The magnitude of gravitational potential on the $x-$ axis at a distance $x$, taking its value to be zero at infinity, is

Two rods of same mass and same length $l_0$ but having different coefficient of expansions $\alpha$ and $3\alpha$ are joined at P(see figure). System is placed on frictionless surface. If temperature of whole system is changed by $\Delta T$, the displacement of junction point is