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A rod of mass $m$, length $l$ is held horizontal, using a vertical string through its centre. If it is turned a little, the frequency of oscillation will be proportional to- [$C$-torsional constant of the string]

Six particles situated at the corners of a regular hexagon with side ${}^{\prime }{a}^{\prime }$ move at a constant speed ${}^{\prime }{v}^{\prime }$. Each particle maintains a direction towards the particle at the next corner. The time taken by the particles to meet each other is

A marble is to be thrown horizontally from a height of $19.6\text{cm}$ above the ground so that it hits another marble on the ground $2\text{m}$ away. The velocity with which the marble should be thrown is

In which time duration is the (magnitude of velocity) speed of the particle increasing?

The system starts from rest and block $A$ attains a velocity of $5\text{m/s}$ after it has moved $5\text{m}$ towards the right. Assuming the arrangement to be frictionless everywhere and pulley & strings to be light, find the value of the constant force $F$ applied on block $A$. (Take $g=10m/s^2$)

The velocity at maximum height of a projectile is half of its initial velocity of projection. the angle of projection is

In which transition ,one quantum of energy is emitted? Explain

(Multiple correct answer type)

A) n= 4 to n= 2 . B) n=3 to n=1 . C) n=4 to n=1 D)n=2 to n=1

A particle, after starting from rest experiences constant acceleration for $20\text{seconds}$. If it covers a distance of $S_1$ in first $10\text{seconds}$ and distance $S_2$ in next $10\text{seconds}$, then

A ball is moving with velocity $2\text{m/s}$ towards a heavy wall approaching the ball with a speed $1\text{m/s}$ as shown in figure. Assuming collision to be elastic, find the velocity of the ball immediately after the collision.
(Considering the initial direction of motion of ball to be $+ve$).

An electron with velocity v is found to have a certain value of de Broglie wavelength. The velocity that the neutron should possess to have the same de Broglie wavelength is-

A wire carries a steady current of 2.4 A. A straight section of the wire is 0.75 m long and lies along the x axis within a uniform magnetic field, B = (1.6 k) T. If the current is in the + x direction, what is the magnetic force on that section of wire?

The threshold wavelength for a metal with work function $W_0$ is ${\lambda }_0$. What is the threshold wavelength for a metal whose work function is $\frac{W_0}{2}$?

If a charge of $500\mu C$ is given to a isolated thin conducting plate and $200\mu C$ gets reside on one of its face, what will be the charge on its other face?

An artificial satellite of mass M & radius $R$ is revolving in a circular orbit of radius $r$. $g$ is acceleration due to gravity. Time period of revolution is ($K$ is a dimensionless unit)

Postulate of kinetic theory is

The displacement x of a particle varies with time according to the relation $x=\frac{a}{b}(1-e^{-bt})$. Which of the following statements is correct?

A person can see clearly only up to a distance of $30\text{cm}$. He wants to read a book placed at a distane of $50\text{cm}$ from his eyes. What is the power of the lens he requires for his spectacles?

In the following, which one of the diodes is reverse biased?

A particle is thrown up inside a stationary lift of sufficient height and the time of flight is $T$. Now it is thrown again with same initial speed $V_0$ with respect to the lift. At the time of second throw, lift is moving up with speed $V_0$ and uniform acceleration $g$ (where $g$ is the the acceleration due to gravity). The new time of flight will be.

A liquid cools down from ${70}^{o}C$ to ${60}^{o}C$ in 5 minutes. The time taken to cool it from ${60}^{o}C$ to ${50}^{o}C$ will be

A swimmer wishes to cross a river flowing at a rate of $2m/s$. His speed with respect to still water is $4m/s$. What angle (in degrees) should the swimmer make with the vertical so that he reaches the exact opposite of the point of his start?

A capacitor is formed by two square metal-plates of edge a, separated by a distance d. Dielectrics of dielectric constants $K_1$ and $K_2$ are filled in the gap as shown in figure (31-E25). Find the capacitance.

In a hypothetical system of particles a mass $m$ with charge $-3q$ is moving around a very heavy particle having charge q. Assuming Bohr’s model to be true to this system, the orbital velocity of mass $m$ when it is nearest to heavy particle is

The acceleration time graph for the object whose displacement time graph is shown below is?

A solid cylinder rolls down a fixed inclined plane of height 'h' and inclination $\theta$. Calculate the time taken to reach bottom?

{Assume the mass be M and radius be R}

Sir , current depends on frame of reference . ??

In a horizontal pipeline of uniform area of cross-section, $2\times {10}^{-2}\text{J/kg}$ is the change in kinetic energy per $\text{kg}$ of the kerosene oil flowing through the pipe of length $1500\text{m}$. What will be the pressure drop between the end points of the pipe? (Take density of kerosene oil as $850{\text{kg/m}}^3)$

A particle of mass 100 g is fired with a velocity $20mse{c}^{-1}$ making an angle of ${30}^{\circ }$ with the horizontal. When it rises to the highest point of its path then the change in its momentum is

An infinite ladder is constructed with 1 $\Omega$ and 2$\Omega$ resistors as shown in figure (32-E22). (a) Find the effective resistance between the points A and B. (b) Find the current that passes through the 2$\Omega$ resistor nearest to the battery. Figure 32 - E22

A balloon initially at rest start rising with constant acceleration of $10{\text{m/s}}^2$. After $2\text{s}$ a particle drops from the balloon. After further $2\text{s}$, match the following (Take $g=10{\text{m/s}}^2$ )
$\begin{array}{cc}\text{Table-1}& \text{Table-2}\\ \text{(A) Height of particle from ground is}& \text{(P) Zero}\\ \text{(B) Speed of particle is}& \text{(Q) 10 SI units}\\ \text{(C) Displacement of particle is}& \text{(R) 40 SI units}\\ \text{(D) Acceleration of particle is}& \text{(S) 20 SI units}\end{array}$

An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively $R_e,R_p,R_d$ and $R_{\alpha }$. It follows that

A body of mass 5 kg is moving in a circle of radius 1m with an angular velocity of 2 radian/sec. The centripetal force is

In 1911, the physicist Ernest Rutherford discovered that atoms have a tiny, dense nucleus by shooting positively charged particles at a very thin gold foil. A key physical property which led Rutherford to use gold was

Two circuits have mutual inductance of $0.09H$. Average e.m.f. induced in the secondary circuit by a change of current from $0$ to $20A$ in $0.006s$ in primary circuit will be

A metal surface of work function 1.07 eV is irradiated with light of wavelength 332 nm. The retarding potential required to stop the escape of photo-electrons is

A cylindrical shell of length L and radius R is uniformly charged with charge Q. This shell is rotating at angular velocity $\omega$ about its axis. If L>>R, magnetic field inside shell is

If a man travels 10 $km$ towards north, then he turns towards east and travels 5 $km$ and again he turns toward south and travels 3 $km$, then what is the coordinate of man with respect to its initial position.(Assume $X-axis$ is towards East, $Y-axis$ is towards North)

A transverse wave is described by the equation $Y=Y_{0}sin2\pi (ft-\frac{x}{\lambda })$ . The maximum particle velocity is four times the wave velocity if

Block A of mass 2m, B and C each of mass m are in equilibrium and at rest shown in the figure. The spring balance, pulley and strings are mass less. Now, a force mg is applied on block C in downward direction. Find the new reading of spring balance. Assume all pulleys to the frictionless.