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The moment of inertia of thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is not equal to (Given $I_1,I_2,I_{3}and{I}_4$ respectively, are the moments of inertia about axes 1,2,3and 4 which are in the plane of the plate)

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A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $\omega$ is an example of a non-inertial frame of reference. The relationship between the force ${\overrightarrow{F}}_{\text{rot}}$ experience by a particle of mass $m$ moving on the rotating disc and the force ${\overrightarrow{F}}_{\text{in}}$ experienced by the particle in an inertial frame of reference is

${\overrightarrow{F}}_{\text{rot}}={\overrightarrow{F}}_{\text{in}}+2m({\overrightarrow{v}}_{\text{rot}}\times \overrightarrow{\omega })+m(\overrightarrow{\omega }\times \overrightarrow{r})\times \overrightarrow{\omega },$



where ${\overrightarrow{v}}_{\text{rot}}$ is the velocity of the particle in the rotating frame of reference and $\overrightarrow{r}$ is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter of a disc of radius $R$ rotating counterclockwise with a constant angular speed $\omega$ about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the $x-$axis along the slot, the $y-$ axis perpendicular to the slot and the $z-$ axis along the rotation axis $\overrightarrow{\omega =\omega \overrightarrow{k}}$. A small block of mass $m$ is gently placed in the slot at $\overrightarrow{r}=\left(R/2\right)\overrightarrow{i}$ at $t=0$ and is constrained to move only along the slot.





The net reaction of the disc on the block is

The MOI of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through point

An ________________ is the path through which the electric current passes.

In Davisson-Germer experiment, as shown below, where electrons are reflected from a crystal plane.





If at angle $i$, the peak diffraction is observed, the de Broglie wavelength of electrons can be calculated by

At a given instant, $A$ is moving with velocity of $5m/s$ upwards. What is velocity of $B$ at that time ?

Photo cells are used for the

A mass-spring system oscillates such that the mass moves on a rough surface having coefficient of friction $\mu$. It is compressed by a distance $a$ from its normal length and, on being released, it moves to a distance $b$ from its equilibrium position. The decrease in amplitude for one half-cycle $(-a\text{to}b)$ is

A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to

In the figure shown, a thin light inextensible string is wrapped aroung a uniform disc. One end of the string is fixed to the ceiling of the lift and the other end is fixed to the circumference of the disc. Acceleration ${}^{\prime }{a}^{\prime }$ of the lift is such that the centre of the disc does not move with respect to the ground. Find the value of $\frac{a}{g}$. (Assume the string does not slip on the pulley)

If block $A$ is moving horizontally with velocity $v_A$, then find the velocity of block $B$ at the instant shown in figure.

$\text{The resultant of the three vectors}\overrightarrow{OA},\overrightarrow{OB}and\overrightarrow{OC}\text{shown in figure is},$

The compressibility of a material is

If $g\left(x\right)=1+\sqrt{x}$ and $f\left(g\right(x\left)\right)$ $=3+2\sqrt{x}+x,$ then the function $f\left(x\right)$ in $a{x}^2+b$ form is

The current flowing through the Zener diode in the given circuit is

What is the concept of resistors in series?How can connecting a resistor having the effective resistance of two resistors in series have the same effect as connecting both the individual resistances in series. The current can only be reduced after it flows through the resistor, right?

For e.g.,In a circuit,I want to connect a resistor inorder to protect a bulb from burning out,.But,it doesn't matter whether the resistor is connected before or after the bulb. How is this possible?

A capillary tube of radius $r$ and length $3h$ is immersed in water. The water rises up to a height $h$. The corresponding mass is $m$. What mass of water will rise in the capillary if the radius of the tube is halved?

A packet is released from a rising balloon accelerating upwards with acceleration a. The acceleration of the packet , first after iyiis released is.

A square frame of edge $5\text{cm}$ is placed with its positive normal making an angle of ${60}^{\circ }$ with a uniform electric field of $200\text{N/C}$. Find the electric flux through the surface bounded by the frame.

Two blocks $m_1=4kg$ and $m_2=2kg$ are connected by a weightess rod on a plane having inclination of ${37}^{\circ }$. The coefficient of dynamic friction for blocks $m_1$ and $m_2$ with the inclined plane is $\mu =0.2$. Assume
${\mu }_k={\mu }_s=0.2$ and g=10 ${ms}^{-2}$. Then the common acceleration of the two blocks and the tension in the rod will be:

An overhang beam of uniform EI is loaded as shown in the figure below. the deflection at the free end will be

A myopic person can see things clearly if they lie between 8 cm and 100 cm from his eye. The lens will enable him to see the moon distinctly if its focal length is:

A long solenoid is fabricated by closely winding a wire of diameter $0.5\text{mm}$ over a cylindrical non-magnetic frame so that the successive turns nearly touch each other. What would be the magnetic field $B$ at the center of the solenoid if it carries a current of $2.5\text{A}$?

A sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T, the mass of each molecule is m. The expression for the density of gas is (k = Boltzmann constant)

A photo-cell is illuminated by a source of light placed at distance d from cell. Graph of photo current I vs. d is best represented by

In Young's double slit experiment, the intensity of each source is $I_0$. The resultant intensity at a point on screen, where path difference is $\frac{3\lambda }{4}$, is,

The unit vector in the direction of $2\hat{i}+3\hat{j}+\hat{k}$ is

For a given solenoid, a constant current of $0.2\text{A}$ is flowing, initially there were $500$ turns for $0.5\text{m}$ length of solenoid. What will be the ratio of magnetic field at the centre of solenoid if the number of turns is increased to $2000$ and length $1.5\text{m}$ keeping the current constant.