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Assuming the string to be inextensible and pulley and surface to be frictionless, the speed of block B in the pulley block system as shown in figure is

Three rings are placed in the same plane as shown. Calculate the MI w.r.t the given axis.

Two conducting circular loops of radii $R_{1}and{R}_2$ are placed in the same plane with their centres coinciding. If $R_1\gg R_2$, the mutual inductance M between them will be directly proportional to

Which of one is correct

A uniform solid sphere of mass M and radius a is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2 a. the ratio of gravitational field at a distance $\frac{3}{2}$ a froth the centre to $\frac{5}{2}$ a from the centre is..

If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ , then the value of $\text{‘}{c}^{\prime }$ is

Find the decrease in the volume of a sample of water from the following data. Initial volume = 1000 cm³, initial pressure = 10⁵ N m^-2, final pressure = 10⁶ N m^-2, compressibility of water = 50 x 10^-11 m² N^-1.

The planet mercury is revolving in an elliptical orbit around the sun as shown in the figure. The kinetic energy of mercury will be greater at

In a simple microscope, if the final image is located at infinity then its magnifying power is; ($D$ is the least distance for distinct vision in the simple microscope)

A vector is represented by $3\hat{i}+\hat{j}+2\hat{k}$. Its length in $XY$ plane is

A clock is in x- y plane. Find angular velocity of second hand of a clock (in rad/s).

Two stars, each of mass m and radius R, are approaching each other for a head-on collision. They start approaching each other when their separation is r >> R. If their speed at this separation is negligible, the speed with which they collide would be

A uniform metal rod is used as a bar pendulum. If the room temperature rises by $10{}^{\circ }\text{C}$, and the coefficient of linear expansion of the rod is $2\times {10}^{-6}/{}^{\circ }\text{C}$, the period of the pendulum will have a percentage increase of

A block of mass $m$ is placed on a surface with a vertical cross-section represented by the equation $y=\frac{x^3}{6}$. If the coefficient of static friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is

A stone is dropped from $25\text{th}$ storey of a multistorey building and reaches the ground in $5\text{s}$. How many storey of the building will the stone cover in first second, if the height of each storey is same?

(Take $g=10m/s^2$)

A prism $(\mu =1.5)$ has the refracting angle of ${30}^{\circ }$. The deviation of a monochromatic ray incident normally on its one surface will be $(sin{48}^{\circ }{36}^{\prime }=0.75)$

A long straight wire, carrying current $I$, is bent at its midpoint to form an angle of ${45}^{\circ }$. Induction of magnetic field at point $P$, distant $R$ from point of bending is equal to

In young's double slit experiment, the two slits act as coherent sources of equal amplitude A and of wavelength $\lambda .$ In another experiment with the same set up, the two slits are sources of equal amplitude A and wavelength $\lambda$ but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case of that in the second case is

If the displacement of particle at any time $t$ is given by $s=ut+\frac{1}{2}a{t}^2$ where $u$ is initial velocity (constant) and $a$ is acceleration (constant) then, velocity of particle at any time $t$ will be

Two speakers are separated by a distance of $3\text{m}$. A person stands at a distance of $4\text{m}$, directly in front of one of the speakers. If $n$ stands for any integer, find the frequencies (in audible range) for which the listener will hear a minimum sound intensity. Speed of sound in air is $320\text{m/s}$.

In figure both the pulleys are massless and frictionless. A force $F$ (of any possible magnitude) is applied in horizontal direction. There is no friction between $M$ and the ground. ${\mu }_1$ and ${\mu }_2$ are coefficients of friction as shown between the blocks. Column I gives the different relations between ${\mu }_1$ and ${\mu }_2$ and Column II is regarding the motion of $M$. Match the columns.





$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i. If}{\mu }_1={\mu }_2=0& \text{a. may accelerate towards right}\\ \text{ii. If}{\mu }_1={\mu }_2\ne 0& \text{b. may accelerate towards left}\\ \text{iii. If}{\mu }_1>{\mu }_2& \text{c. does not accelerate}\\ \text{iv. If}{\mu }_1<{\mu }_2& \text{d. may or may not accelerate}\end{array}$

If a particle is projected from origin and it follows the trajectory $y=x-\frac{1}{2}{x}^2$, then the time of flight is ($g$ = acceleration due to gravity)

A ball of mass $m$ is released from rest at $\text{A}$ as shown in the figure. Find the minimum height $h$, so that ball will just complete the circular motion on the track (all surfaces are smooth).

The wires A and B shown in the figure are made of the same material, and have radii r_A and r_B respectively. The block between them has a mass m. When the force F is mg/3, one of the wires breaks.

If $\overrightarrow{r}.\hat{i}=\overrightarrow{r}.\hat{j}=\overrightarrow{r}.\hat{k}$ and $|r|=2$, then find $\overrightarrow{r}$.

What is the equivalent resistance of an ammeter that has a coil resistance of $1k\Omega$, and a shunt resistance of $1\Omega$?

When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from $0.26\mu \text{m}$ to $0.13\mu \text{m}$ Then ratio of the emissive power of the body at respective temperature is

The figure below shows the path of white light’s rays which leave in phase from two small sources $S_1$ and $S_2$ and travel to a point X on a screen. The path difference is $S_{2}X-S_{1}X=8.7\times {10}^{-7}m$. What wavelength of light gives complete destructive interference at X?

A particle moves along a semicircle of radius $10\text{m}$ in 5 seconds. The magnitude of average velocity of the particle is

In the diagram, resistance between any two junctions is R. Equivalent resistance across terminals A and B is

If the speed of the wave shown in the figure is 330 m/s in the given medium, then the equation of the wave propagating in the positive x - direction will be -(all quantities are in MKS units)

A sky wave with a frequency 55 MHz is incident on D-region of earth's atmosphere at ${45}^{\circ }$. The angle of refraction is (electron density for D-region is 400 electron/${cm}^3$)

A solid sphere $A$ of mass $m$ rolls without slipping on an inclined plane of inclination ${30}^{\circ }$. Coefficient of friction between the inclined plane and the sphere is $\mu$. Then, which of the following options is satisfied when the sphere undergoes pure rolling motion?

A rigid spherical body is spinning around an axis without any external torque. Due to temperature its volume increases by 3%. Then percentage change in its angular speed is

A heavy piece of machinery is raised by sliding it a distance of d=10m along a plank oriented at an angle, $\theta ={60}^{\circ }$ as shown in figure. How far has it moved vertically and horizontally?

One end of a horizontal cylindrical glass rod $(\mu =1.5)$ of radius 5.0 cm is rounded in the shape of a hemisphere. An object 0.5 mm high is placed perpendicular to the axis of the rod at a distance of 20.0 cm from the rounded edge. Locate the image of the object and find its height.

A jet of water is projected at an angle $\theta ={45}^{\circ }$ with the horizontal from a point which is at a distance of $x=15\text{m}$ from a vertical wall as shown in the figure. If the speed of projection is $10\sqrt{2}\text{m/s}$, find out the height from ground at which the water jet strikes vertical wall. Take $g=10{\text{m/s}}^2$

A rocket of mass $120\text{kg}$ has $280\text{kg}$ of fuel is ready for the take off. The relative exhaust velocity of the fuel is $1.8\text{km/s}$ and the rate of consumption of the fuel is $2\text{kg/s}$. Calculate the ultimate vertical speed gained by the rocket. (Take $g=9.8{\text{m/s}}^2$)

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

Find $V_A-V_B$ in steady state

A system of two blocks $A$ and $B$ are connected by an inextensiible massless string as shown in figure. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass $m$ moving with a velocity $u$ as shown in the figure hits block $B$ and gets embedded into it. Then find out the impulse imparted by tension force to the block of mass $3m$, immediately after the collision takes place.

The dimensions of $({\mu }_0{ϵ}_0{)}^{\frac{-1}{2}}$ are

An organ pipe closed at one end has a fundamental frequency of $1500\text{Hz}$. The maximum number of overtones generated by this pipe which a normal person can hear is

Two cars, initially at a separation of $12\text{m}$, start simultaneously. First car "$A$", starting from rest, moves with an acceleration $2{\text{m/s}}^2$, whereas the car "$B$" which is ahead, moves with a constant velocity $1\text{m/s}$ along the same direction. Find the time when the car "$A$" overtakes car "$B$".

Match Column - $\text{I}$ with Column -$\text{II}$

$\begin{array}{cc}\text{Column - I}& \text{Column - II}\\ \text{i.Velocity of a particle following}& \text{(p)}\alpha \\ \text{equation}x=u(t-8)+\alpha (t-2{)}^2& \\ \text{at}t=0& \\ \text{ii.Acceleration of a particle moving according to equation}& \text{(q)}2\alpha \\ x=u(t-8)+\alpha (t-2{)}^2\text{at}t=0& \\ \text{iii.Velocity of the particle moving}& \text{(r) u}\\ \text{according to equation}x=ut+& \\ 5\alpha t^2\ln (1+\frac{t}{2})+\alpha t^2\text{at}t=0& \\ \text{iv.Acceleration of the particle moving}& \text{(s)}u-4\alpha \\ \text{according to the equation}x=ut+& \\ 5\alpha t^2(1+\frac{t}{2})+\alpha t^2\text{at}t=0& \end{array}$