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A potential barrier of $0.50\text{V}$ exists across a $p-n$ junction. The depletion region is $5\times {10}^{-7}\text{m}$ wide. An electron with speed $5\times {10}^5{\text{ms}}^{-1}$ approaches the $p-n$ junction from the $n-$ side with what speed will it enter the $p-$ side ?

A small block is connected to one end of two identical massless strings of length 16 cm each with their other ends fixed to a vertical rod. If the ratio of tensions be 4:1, then what will be the angular velocity $\omega$ of the block.

A circular racing track of radius $300\text{m}$ is banked at an angle of ${17}^{\circ }$ with the horizontal. If the coefficient of static friction $\left({\mu }_s\right)$ between the wheels of the racing car and the road is $0.2$, what is the maximum permissible speed to avoid slipping? Take $g=10{\text{m/s}}^2$. Use the given data: $\tan {17}^{\circ }=0.30,\sin {17}^{\circ }=0.29,\cos {17}^{\circ }=0.96$ and $\frac{0.50}{0.94}\simeq 0.5$

Two ships are 10 km apart on a line joining south to north. The one farther north is steaming west at $20{\text{km h}}^{-1}$. The other is steaming north at $20{\text{km h}}^{-1}$. What is their distance of closest approach? How long do they take to reach it?

A long straight metal rod has a very long hole of radius $a$ drilled parallel to its axis, as shown in the figure. If the rod carries a current $i$, find the value of magnetic induction on the axis of the hole, where $\text{OC}=c.$

Two inclined planes $OA$ and $OB$ having inclination (with horizontal) ${30}^{\circ }$ and ${60}^{\circ }$, respectively, intersect each other at $O$ as shown in figure. A particle is projected from point $P$ with velocity $u=10\left(\sqrt{3}\right){\text{ms}}^{-1}$ along a direction perpendicular to the plane $OA$. If the particle strikes the plane $OB$ perpendicular at $Q$, calculate the displacement $PQ$.

A
short bar magnet placed with its axis at 30º with a uniform
external
magnetic field of 0.25 T experiences a torque of magnitude equal to
4.5 × 10⁻²
J. What is the magnitude of magnetic moment of the magnet?

Two identical long conducting wires $AOB$ and $COD$ are placed at right angle to each other, with one above other such that ${}^{\prime }{O}^{\prime }$ their common point for the two. The wires carry $I_1\text{and}{I}_2$ currents respectively. Point ${}^{\prime }{P}^{\prime }$ is lying at distance ${}^{\prime }{d}^{\prime }$ from ${}^{\prime }{O}^{\prime }$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point ${}^{\prime }{P}^{\prime }$ will be

1. 450.45

A block of mass $2\text{kg}$ rests on a rough inclined plane making an angle of ${30}^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.7$. The frictional force on the block is

An object projected vertically up from the earth's surface with velocity $\sqrt{gR}$, where $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the surface of earth. Find the maximum height reached by the object.

A simple pendulum has time period $T_1$. The point of suspension is now moved upward according to the relation $y=k{t}^2(k=1m/s^2)$, where y is the vertical displacement. The time period now becomes $T_2$. The ratio of $\frac{T_1^2}{T_2^2}$ is considered to be x. Then the value of 5x is ___. (Take $g=10m/s^2$)

If light of wavelength ${\lambda }_1$ is allowed to fall on a metal, then kinetic energy of photoelectrons emitted is $K_1$. If wavelength of light changes to ${\lambda }_2$, then kinetic energy of electron changes to $K_2$. Then, work function of the metal is

Which of the following decreases in motion along a straight line with constant retardation?

consider an ice cube of edge 1.0 cm kept in a gravity -free hall. Find the surface area of the water when the ice melts. Neglect the difference in densities of ice and water.

The angular speed of seconds needle in a mechanical watch is

Ablock of mass m = 15 kg is suspended in an elevator with the help of three identical light elastic cords (spring constant k = 100 N/m each) attached vertically. Cord 1 is tied to the ceiling of the elevator and the other two cords 2 and 3 are tied to the elevator floor as shown in the figure. When the elevator is stationary the tension force in each of the lower cords is T = 7.5 N. Take g = 10 $m/s^2$. If now the elevator starts moving with given four accelerations shown in column I and Column II gives the displacement of the block with respect to elevator when it is accelerating. Column III gives tension in the cords when elevator is accelerating.

Column III represents the tension in chord 2.

Heat at the rate of 200 W is produced in an X-ray tube operating at 20 kV. Find the current in the circuit. Assume that only a small fraction of the kinetic energy of electrons is converted into X-rays.

A piezoelectric type 50 MPa full-scale pressure sensor with built-in electronics has a sensitivity of 100 mV per MPa. If this sensor is subjected to a static pressure of 10 MPa then its output will be

Particle $P$ shown in figure is moving in a circle of radius $R=10cm$ with linear speed $v=2m/s$. Find the angular speed of particle about point $O$

A bird perches on a bare high power line, and nothing happens to the bird. A man standing on the ground touches the same line and gets a fatal shock. Why?

The distance between the plates of a charged parallel plate capacitor is $5\text{cm}$ and the electric field inside the plates is $200\text{V/cm}$. An uncharged metal plate of same length and width $2\text{cm}$ is inserted between the capacitor. The voltage across capacitor after insertion of the plate is

A mass of $10\text{kg}$ is suspended by a rope of length $4\text{m}$, from the ceiling. A force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of ${45}^{\circ }$ with the vertical. Then $F$ equals:

(Take $g=10{\text{ms}}^{-2}$ and the rope to be massless)

What happens if a vector is multiplied by the number 2?

A child is sitting on a swing. Its minimum and maximum heights from the ground are $0.75\text{m}$ and $2\text{m}$ respectively, its maximum speed will be

Seven capacitors, each of capacitance $2\mu F$, are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right)\mu F$. Which of the combinations, shown in figure below, will achieve the desired value ?