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A photon, an electron and a uranium nucleus all have the same wavelength. The one with the most energy

Particle A is released from a point P on a smooth inclined plane inclined at an angle $\alpha$ with the horizontal. At the same instant another particle B is projected with initial velocity $u$ making an angle $\beta$ with the horizontal. Both the particles meet again on the inclined plane. Find the relation between $\alpha$ and $\beta$

The temperature inside a refrigerator is $t_2^{}°C$ and the room temperature is $t_1^{}°C$. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be

Neena goes around a circular track that has a diameter of $7m$. If she runs around the entire track for a distance of $50m$, what is her angular displacement?

A uniform disc of mass $M$ and radius $R$ is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc as shown in figure below. If we hang a body of mass $m$ with the cord, it has acceleration $a$ as shown in figure. Find the angular acceleration of the disc $\left(\alpha \right)$.

A ball is made of a material of density $\rho$ where, ${\rho }_{\text{oil}}<\rho <{\rho }_{\text{water}}$ with ${\rho }_{\text{oil}}$ and ${\rho }_{\text{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium positions?

A constant force of $10\text{N}$ applied on the flywheel of radius $20\text{cm}$ as shown in figure. If the flywheel covers an angular displacement of ${60}^{\circ }$. Calculate the work done on the flywheel.

(Assume $\pi =3$)

An isosceles right angled triangle of side $5\text{cm}$ is cut from a circular disc of radius $5\text{cm}$ as shown in the figure. What will be the coordinates of the centre of mass of the remaining disc? Origin is taken at the centre of the circular disc. Consider the material to be of uniform density.

If $F=\frac{GmM}{r^2}$, then $\frac{dF}{dr}=?$

Three blocks of mass $10\text{kg}$, $5\text{kg}$ and $8\text{kg}$ are connected to each other with a light string and placed on a wedge with angle of inclination ${30}^{\circ }$. A force F applied on the string causes all the three blocks to move with a common acceleration of $2m/s^2$. If the coefficient of friction between the blocks and the surface of the wedge is $0.2$, then what is the tension at the three points $A,B$ and $C$?

If $a=(3t^2+2t+1)m/s^2$ is the expression according to which the acceleration of a particle moving along a straight line varies, then the change in velocity after 3 seconds of its start is

A square lamina of mass density $\left(\sigma \right)=10{\text{kg/m}}^2$ and side length $2\text{m}$ is rotated about an axis passing through one of it’s side as shown in figure. Find the moment of inertia of the lamina about this axis.

A body of mass $10\text{kg}$ moving with velocity of $10\text{m/s}$ hits another body of mass $30\text{kg}$ moving with velocity $3\text{m/s}$ in same direction. The co-efficient of restitution is $\frac{1}{4}$. The velocity of centre of mass after collision will be

An incompressible liquid is flowing through the horizontal pipe as shown in the figure. Pipe $1$ is connected to the pipe $2$ and pipe $3$. The flow of liquid through the pipe $1$, pipe $2$ and pipe $3$ are $8\text{m/s},6\text{m/s}$ and $1.1\text{m/s}$ respectively. If cross-section area of pipe $1$ and pipe $2$ are $1{\text{m}}^2$ and $0.8{\text{m}}^2$, find the area of cross-section of pipe $3$.

Three capacitors each of capacitance 1μF are connected in parallel. To this

combination, a fourth capacitor of capacitance 1μF is connected in series.

The resultant capacitance of the system is

The work done to raise a mass $m$ from the surface of the earth to a height $h$, which is equal to the radius of the earth is

In the given figure, masses of $A$ and $B$ are $5\text{kg}$ and $10\text{kg}$ respectively. Coefficient of friction between blocks is 0.2. If the lower block is pulled rightwards with a constant force, $F=50\text{N}$, time elapsed before block $A$ falls off block $B$ is: (There is no friction between block $B$ and surface) and neglect the size of $A$)

A ring of radius $1\text{m}$ is performing combined translational and rotational motion on a frictionless horizontal surface with an angular velocity of $3\text{rad/s}$ as shown in figure. Find out velocity of the point $A$ in $\text{m/s}$, if the speed of the lowest point $V_P$ is $1\text{m/s}$.

A stretched string is vibrating according to the equation $y=5\sin \left(\frac{\pi x}{2}\right)\cos 4\pi t$, where $y$ and $x$ are in $\text{cm}$ and $t$ is in $\text{sec}$. The distance between two consecutive nodes on the string is

An ice skier is sliding from a point $\text{A}$ as shown in the figure below. If the slider starts from rest and acceleration due to gravity is $10\text{m}/s^2$, then what is the velocity of the skier at point $\text{B}$.

In the shown figure, $X_c=100\Omega$, $X_L=200\Omega$ and $R=100\Omega$. The effective current through the source is

The speed of a transverse wave travelling through a wire having a length $50\text{cm}$and mass $5.0\text{g}$ is $80\text{m/s}$. The area of cross-section of the wire is $1.0{\text{mm}}^2$ and its Young's modulus is $16\times {10}^{11}{\text{N/m}}^2$. Find the extension in the wire with respect to its natural length.

A vertical glass tube, closed at the bottom, contains a mercury column of length $L_0$ at $0^{\circ }\text{C}$. If $\gamma$ is the coefficient of cubical expansion of mercury $\alpha$ the coefficient of linear expansion of glass, the length of the mercury column when the temperature rises to $t^{\circ }\text{C}$ is (assuming that $t$ not more than ${100}^{\circ }\text{C}$)

Water rises upto 10 cm height in a long capillary tube. If this tube is immersed in water so that the height above the water surface is only 8 cm, then

A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time $\frac{t}{2}$ s.

The horizontal component of a force of $10N$ inclined at ${30}^o$ to vertical is

The rear side of a truck is open and a box of $40\text{kg}$ mass is placed $5\text{m}$ away from the open end as shown. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road, the truck starts from rest and accelerates with $2{\text{ms}}^{-2}$. At what distance from the starting point does the box fall off the truck (i.e., distance travelled by the truck)? [Ignore the size of the box]

A silver ingot weighing 2.1 kg is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of silver is 10.5. The tension in the string in kg-wt is

Force-time$\left(\text{F - t}\right)$ graph of a rocket of mass 1000 kg shown below describes the force on the rocket. Neglecting gravity, the velocity of rocket $16\text{s}$ after starting from rest is

A wheel rotates with a constant angular acceleration of 2.0 $\frac{rad}{s^2}$. If the wheel starts from rest, how many revolutions will it make in the first 10 seconds?

In the given figure, a ray of light $1\text{cm}$ above the principal axis get reflected from a concave mirror and intersect the principal axis at $Y$. Find the length $PY$ if the radius of curvature of the mirror is $2\text{cm}$.

If time of flight of a projectile is 10 seconds. Range is 500 meters. The maximum height attained by it will be

A bullet is fired with a velocity of $196m{s}^{-1}$ at an angle ${30}^{\circ }$ with the horizontal. Calculate the maximum height attained by the bullet. (Take $g=9.8m/s^2)$

A body traveling along a straight line traversed first one third of the total distance with a velocity $3\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The mean velocity over the whole time of motion is

A body of mass 2 kg has an initial velocity $v_i=(\hat{i}+\hat{j})m{s}^{-1}$. After the collision with another body its velocity becomes $v_f=(5\hat{i}+6\hat{j}-\hat{k})m{s}^{-1}$. If the impact time is 0.02 s, the average force of impact on the body (in newton) is

Current sensitivity of a moving coil galvanometer is $5div/mA$ and its voltage sensitivity (angular deflection per unit voltage applied) is $20div/V$. The resistance of the galvanometer is

A system of 3 blocks of masses of $10kg,20kg,30kg$ respectively, having flat surfaces of contact with coefficients of friction given in the figure are at rest initially. If a constant horizontal force of $F=100N$ is acting on $10kg$ block as shown in figure, then the magnitude of acceleration of the $20kg$ block with respect to the ground is (Take $g=10m/s^2)$

When the temperature is increased the angle of contact of a liquid

What is the stopping potential when the metal with work function 0.6 eV is illuminated with the light of 2 eV

The vibration of air in an open organ pipe of length $30\text{cm}$ is represented by $\Delta p=8\sin \left(\frac{2\pi x}{25}\right)\cos \left(48\pi t\right),$ where $x,p\text{and}t$ are in $\text{cm},{\text{N/m}}^2$ and $\text{sec}$ respectively. The excess pressure (pressure over atmospheric pressure) amplitude at $x=10\text{cm}$ is

[ Take $\sin \left(\frac{4\pi }{5}\right)=0.587$ ]

A constant force $\overrightarrow{F_1}=(2\hat{i}-4\hat{j})\text{N}$ displaces a particle from $(1,-1,2)$ to $(-1,-1,3)$ and then another force of $\overrightarrow{F_2}=(3\hat{i}+4\hat{j})\text{N}$, displaces it from $(-1,-1,3)$ to $(5,5,5)$ (displacements being measure in metre). Find the total work done.

The coefficient of static friction is $0.2$ between block $A$ of mass $2\text{kg}$ and the table as shown in the figure. What would be the maximum mass value of block $B$ so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless $(g=10{\text{m/s}}^2)$

A body is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration $a$ directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration $a$ vertically. The tension in the string is equal to -

A gas of density $\rho$ flows with velocity $v$ along a pipe of cross - sectional area $S$ and bent to an angle of ${90}^{\circ }$ at point $A$. What force does the gas exert on the pipe at point $A$ ?

A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be ${\frac{1}{8}}^{th}$ to its value at the centre of the coil, is