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A block of mass $2\text{kg}$ moving with speed $5\text{m/s}$ collides with another block of mass $4\text{kg}$ at rest. The lighter block comes to rest after the collision. Find the coefficient of restitution $\left(e\right)$. (Neglect all other external force)

The stream of electrons from a heated filament was passed between two charged plates kept at a potential difference $V$. If e and m are charge and mass of electron respectively, then the value of $\frac{h}{\lambda }$ is:
(where $\lambda$ is the de Broglie wavelength of the electron)

If $\overrightarrow{r}=bt\hat{i}+c{t}^2\hat{j}$ where b and c are positive constants, the velocity vector make an angle of ${45}^{\circ }$ with the x and y axes at t equal to

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

A lighter body and heavier body both are moving with same momentum and are being applied the same retarding force.Their stopping distances and stopping times are $S_1,S_{2}and{t}_1,t_2$ respectively.Then,

The diagram below show regions of equipotential

A platinum wire has a resistance of $10\Omega$ at $0^{\circ }C$ and $20\Omega$ at ${273}^{\circ }C$. Find the value of temperature coefficient of platinum.

Figure shows two rods $A$ and $B$ of same length $L$ and same cross-sectional area $S$ but of different material having coefficient of linear expansion ${\alpha }_1$ and ${\alpha }_2$ respectively. They are clamped between two rigid walls, separated by a distance $2L$. This all refers to temp $t^{\circ }\text{C}$. Find the tension in each rod at temp $2t^{\circ }\text{C}$ (Take the young’s modulus for the two rods to be $Y_1$ and $Y_2$ respectively).

An electron of mass $0.90\times {10}^{-30}kg$ under the action of a magnetic field moves in a circle of 2.0 $cm$ radius at a speed of $3.0\times {10}^{6}m{s}^{-1}$. If a proton of mass $1.8\times {10}^{-27}kg$ has to move in a circle of the same radius in the same magnetic field, then its speed will be $m{s}^{-1}$.

A wire carrying current $I$ has the shape as shown in figure. Linear parts of the wire are very long and parallel to X - axis while semicircular portion of radius $R$ is lying in Y - Z plane. Magnetic field at point O is:

A spring of force constant $K$ is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is $K^{{}^{\prime }}$. Then, they are connected in parallel and the force constant is $K^{\prime \prime }$. Then, $\frac{K^{{}^{\prime }}}{K^{\prime \prime }}$ is

The linear charge density on a dielectric ring of radius $R$ is varying with $\theta$ as $\lambda ={\lambda }_0\cos \left(\theta /2\right)$. The potential at the centre of the ring is

When a uniform metallic wire is stretched the lateral strain produced in it is $\beta$. If $\nu$ and $Y$ are the Poisson's ratio and Young's modulus for the wire, then elastic potential energy density of wire is

Block $A$ of mass $m$ is hanging from a vertical spring having stiffness $k$ and is at rest. Block $B$ of identical mass strikes the block $A$ with velocity $v$ and sticks to it. Then the value of $v$ for which the spring just attains natural lengths is

A force $\overrightarrow{F}=-k(y\hat{i}+x\hat{j})$, where $k$ is a constant, acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken from the origin $(0,0)$ to the point $(a,0)$ and then from the point $(a,0)$ to the point $(a,a)$. The total work done by the force $\overrightarrow{F}$ on the particle is

The potential energy of a system is represented in the first figure. The force acting on the system will be represented by

A light ray is incident at an angle of ${45}^{\circ }$ with the normal to a $\sqrt{2}\text{cm}$ thick plate $(\mu =2.0)$. Find the shift in the path of the light as it emerges out from the plate.

In the figure shown the cart of mass 6m is initially at rest. A particle of mass m is attached to the end of the light rod which can rotate freely about A. If the rod is released from rest in a horizontal position shown, determine the velocity $v_{rel}$of the particle with respect to the cart when the rod is vertical.

What is the Unit of Charge?

Two vehicles are blowing horn at $\frac{320}{3}Hz$. They are moving directly towards each other. $A$ is moving at $10m/s$ and $B$ is moving such that he hears a beat frequency of $5Hz$ at $t=0$. If they are $90m$ apart at $t=0$, at what time (in $sec$) will the vehicles cross each other ? (Take speed of sound = $330m/s$)

A man moves on a straight horizontal road with a block of mass 2 kg in his hand . If he covers a distance of 40 m with an acceleration $0.5m/s^2$, find the work done by the man on the block during the motion.

In an isolated, charged, parallel plate air capacitor, the surface charge density on each plate has a magnitude $\sigma$. A dielectric slab with dielectric constant K is now introduced between the plates. The induced charge per unit area on the surface of the dielectric will be :

Two blocks A and B of masses $2m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively:

Two L-shaped wires are kept over each other as shown. The wire on the left is fixed and the wire on the right is movable on the left wire without any friction. The whole system is in a horizontal plane. Now we make a soap film of surface tension 0.1 N/m in between the wires such that it covers the common quadrilateral area.
If the right wire has a mass of 125 g, then its initial acceleration on being released is

The bulk modulus of water is $2.1\times {10}^{9}N/m^2$. The pressure required to increase the density of water by 0.1 % is

Coefficient of friction between $5kg$ and $10kg$ block is $0.5$. If friction between them is $20N$, the value of force being applied on $5kg$ (in $N$) is (Assume that the floor is frictionless)

A point charge $q$ of mass $m$ is released (displaced slightly) along axis of ring from center of the ring of radius $R$ and having a uniform charge $Q$. Speed of point charge when its acceleration is maximum can be given by

If a spring has time period ‘T’, and is cut into ‘n’ equal parts, then the time period of each part will be

Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index μ is placed on face AC of the prism. The prism is made of glass of refractive index 3/2. The limits of μ for which total internal reflection takes place on face AC is

There is a spherical cavity inside a uniform solid sphere as shown in the figure. Then, for the magnitude of gravitational potential difference V, which of the following is true?

What force is required to stretch a steel wire $1c{m}^2$ in cross section to double its length? (Youngs modulus for steel is $2\times {10}^{11}Pa$)

We have an isolated conducting spherical shell of radius $10cm$. Some positive charge is given to it so that resulting electric field has a maximum intensity of $1.8\times {10}^{6}N{C}^{-1}.$ The same amount of negative charge is given to another isolated conducting spherical shell of radius $20cm$. Now, first shell is placed inside the second so that both are concentric as shown in the figure.

The electric potential at any point inside the first shell is

A laser beam $\lambda =633nm$ has a power of $3mW$. What will be the pressure exerted on a surface by this beam if the cross-section area is $3m{m}^2$? (Assume perfect reflection and normal incidence).

Find the work done in lifting $5$ cement bags, each of mass $25\text{kg}$ to the top of a building of height $50\text{m}$.(consider $g=10m/s^2$)

A uniformly charged rod (with total charge Q) and length l applies a force on other charge Q¹placed on its axis (i.e. along the rod) at a distance 1000l from its centre can be approximated as $\frac{KQ{Q}^1}{(1000l{)}^2}$ The reason it came out to be so is because

A rubber cube of side $5\text{cm}$ has one side fixed while a tangential force equal to $1800\text{N}$ is applied to the opposite face. Find the shearing strain and the lateral displacement of the strained face. Modulus of rigidity for rubber is $2.4\times {10}^6{\text{N/m}}^2$.

A block of mass $10kg$ is placed on a rough horizontal surface whose coefficient of friction is $0.5$. If a horizontal force of magnitude $100N$ is applied on the block, then acceleration of the block will be $[\text{Take}g=10m{s}^{-2}]$

An ideal fluid is flowing in a pipe in a streamline flow. The pipe has a maximum and minimum diameter of $6.4\text{cm}$ and $4.8\text{cm}$ respectively. Find out the ratio of minimum to maximum velocity.

An ideal gas is taken through a cyclic thermodynamic process through four steps. The amount of heat exchanged in the steps are $Q_1=+5960\text{J},Q_2=-5600\text{J},Q_3=-3000\text{J},Q_4=+3600\text{J}$ respectively. The corresponding quantities of internal energy changes are $\Delta U_1=+3760\text{J},\Delta U_2=-4800\text{J},\Delta U_3=-1800\text{J}$ and $\Delta U_4$. Find the value of $\Delta U_4$ and work done during the cyclic process.

State whether true or false: A charge when released in electrostatic field moves along electrostatic field lines.

Three particles of masses $50\text{g},100\text{g}$ and $150\text{g}$ are placed at the vertices of an equilateral triangle of side $2\text{m}$ as shown in the figure. The $(x,y)$ co-ordinates of the centre of mass (in $\text{m})$ will be