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Two bodies of masses of $1\text{kg}$ and $3\text{kg}$ initially at rest are moving with velocities $30\text{m/s}$ and $10\text{m/s}$ towards each other due to mutual force of attraction. What is the velocity of the centre of mass of system?

A polaroid is placed at 45^o to an incoming light of intensity I₀. Now the intensity of light passing through polaroid after polarisation would be

A body of mass $5\text{kg}$ starts from rest and moves in a straight line under the influence of two variable forces $F_1=(10t+\frac{6}{t})\text{N}$ and $F_2=(15-\frac{6}{t})\text{N}$, acting in same direction. Find the power delivered by force $F_1$ at $t=2\text{sec}$.

As shown in the figure, two masses $6\text{kg}$ and $4\text{kg}$ respectively are tied to the ends of a string which passes over a light frictionless pulley. Initially, the masses are at rest and are at the same horizontal level. Now, they are released. Find the distance travelled by their center of mass in $10\text{s}$.

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be

Two discs of radii $4\text{cm}$ and $2\text{cm}$ respectively are attached as shown in the figure. The distance of the new centre of mass of the system from ${\text{C}}_1$ is

Compare the speed of the three particles $A,B$ and $C$ as per the distance-time graph shown below.

Transverse waves are generated in two uniform wires $A$ and $B$ of the same material by attaching their free ends to a vibrating source of frequency $200\text{Hz}$. The cross-sectional area of $A$ is half that of $B$ while the tension on $A$ is twice that on $B$. The ratio of the wavelengths of the transverse waves in $A$ and $B$ is

Find I, $i_1$, and $i_2$.

A body of mass $0.01\text{kg}$ executes simple harmonic motion (SHM) about $x=0$ under the influence of a force $F$ which varies with $x$ as shown in figure. Find the time period of SHM of the body.

You live on a busy street, but as a music lover, you want to reduce the traffic noise. If you install special sound-reflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity $\left(in\frac{w}{m^2}\right)$?

To get the formula of electric field due to a ring at the centre from the formula of electric field due to an arc at centre, replace $\theta$ with .

In the figure shown below, $\overrightarrow{\omega }$ is angular velocity and $\overrightarrow{r}$ is position vector. What is the direction and magnitude of linear velocity.

In an ideal transformer, the voltage and the current in primary coil are $200\text{V}$ and $2\text{A}$ respectively. If the voltage in the secondary coil is $200\text{V}$, then the value of current in the secondary coil will be

A body of density $d_1$ is counterpoised by Mg of weights of density $d_2$ in air of density d. Then the true mass of the body is

Two insulated charged spheres of radii 20cm and 25cmrespectively and

having an equal charge Q are connected by a copper wire, then they are

separated

A person is pulling a mass m from ground on a rough hemispherical fixed surface up to the top of the hemisphere with the help of a light inextensible string as shown in the figure. The radius of the hemisphere is $R$. Find the work done by the tension in the string. Assume that the mass is moved with a negligible constant velocity, $u$. (The coefficient of friction is $\mu$)

The velocity of sound in air is $333\text{m/s}$. In order to produce the second overtone of frequency $999\text{Hz}$ in it, the length of the open organ pipe will be :

In the figure shown, find the direction of friction on blocks B and C at the surface which is common to the blocks B and C respectively.

A cubical block rests on a plane of $\mu =\sqrt{3}$. The angle through which the plane should be inclined to the horizontal so that the block just slides down will be

Two swimmers swim in a stand still lake. First swimmer swims directly across the lake ($30m$ wide) with a velocity of $1.5m/s$, reaches the other end and runs a distance of $10m$ in $10$ seconds along the shore. What should be the velocity of the second swimmer so that he reaches the same point in the same time ?

On seeing enemy ships at a distance of 125 m from the shore, the canons start firing fireballs. The captain of the ship saw the cannon fire. He knows the velocity of the fireballs is 50 m/s. Now in how much time does he have to steer his ship in some other direction so as to save his crew. Use angle of projection as ${30}^{\circ }$. Also find the maximum height that the fireball reaches above water.

A laser beam of pulse power ${10}^{12}$ watt is focussed on an object are ${10}^{-4}{cm}^2$ . The energy flux in watt/ ${cm}^2$ at the point of focus is

A cylinder is rotating with angular velocity ω and angular acceleration α at any instant, while translating with velocity V. Find the net acceleration of point P at this instant (radius of cylinder is R).

Find the $ϵ$ mf induced in the square frame.

A ${}^{238}U$ nucleus decays by emitting an alpha particle of speed ${}^{\prime }{v}^{\prime }m{s}^{-1}$. The recoil speed of the residual nucleus (in $m{s}^{-1}$ ) is:

Rain pouring down at an angle $\alpha$ with the vertical has a speed of $10\text{m/s}$. A girl runs against the rain with the speed of $8\text{m/s}$ and sees that the rain makes an angle $\beta$ with the vertical, then relation between $\alpha$ and $\beta$ is

A block of mass $50kg$ can slide on a rough horizontal surface. The coefficient of friction between the block and the surface is $0.6$. The least force of pull acting at an angle of ${30}^{\circ }$ from the horizontal which causes the block to just slide is

An electromagnetic wave in vacuum has the electric and magnetic field $\overrightarrow{E}$ and $\overrightarrow{B}$, which are always perpendicular to each other. The direction of polarization is given by $\overrightarrow{X}$ and that of wave propagation by $\overrightarrow{k}$. Then

A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ and finally come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is -

Two metallic spheres of radii $1\text{cm}$ and $3\text{cm}$ are given charges of $-1\times {10}^{-2}\text{C}$ and $5\times {10}^{-2}\text{C}$ respectively. If these are connected by a conducting wire (potential on them becomes equal), the final charge on bigger sphere is

What is the emitter current if $I_B=20\mu A$ and $\beta =100$ ?

A block is moving under the influence of a constant force $F=3600\text{N}$. The force acts on the ball for the duration of $0.004\text{h}$. The average impulse imparted by the force is

A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly

The angle of minimum deviation for prism angle $\frac{\pi }{3}$ is $\frac{\pi }{6}$. Calculate the velocity in the material of the prism, if the velocity of light in vacuum is $3.00\times {10}^{8}m{s}^{-1}$.

A person travels $100\text{km}$ in the North direction and then turns right and travels $100\text{km}$. Consider the starting point as origin, North direction as positive y direction and East direction as positive x direction. The final position of the person is

A metal wire is stretched by a load. Then the fractional change in its volume $\frac{\Delta V}{V}$ is proportional to

The potential difference $(V_A-V_B)$ between the points A and B in the given figure is

In vertical circular motion, the ratio of kinetic energy of a particle at highest point to lowest point is (Particle is just completing vertical circular motion)

A total of Q charge flows from resistance R in time interval T such that current vs time graph is obtained as shown in figure. The heat generated in resistance is:

A capacitor having $C=10\mu F$; Potential across plates, V = 10V; Distance between plates 10mm; And area of plates $10c{m}^2$, has air between the plates. What is the force on one of the plates.

A block of mass $10\text{kg}$ is moving with a uniform speed of $20\text{m/s}$ enters onto a rough surface of coefficient of friction $0.8$, the time taken by the block to come to rest is

A square plate of side 'a' is kept below an infinite line charge of charge per unit length $\lambda$ (as shown in figure). Electric flux associated with the plate is $\frac{3\lambda a}{n\pi {ϵ}_o}ta{n}^{-1}\left(\frac{1}{2}\right).$

Here, n is

An object and its real image are located at distances $25\text{cm}$ and $40\text{cm}$ respectively from the two principal focii of a convex lens on either side. The linear magnification of the image is nearly equal to

Time taken by the projectile to reach from $A$ to $B$ is $t$. Then, the distance $AB$ is equal to

The sum of the magnitudes of two forces acting at a point is $18$ and the magnitude of their resultant is $12$. If the resultant is at ${90}^{\circ }$ with the force of smaller magnitude, then what are the magnitudes of the forces?

A ray parallel to $x$ - axis is incident on a spherical reflecting surface of radius $R$ and the reflected ray becomes parallel to the $y$ - axis as shown. Find the coordinates of point $P$.