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A coil of area 10 cm² of 20 turns is placed in uniform magnetic field of 10⁴ gauss. The normal to the plane of the coil makes an angle of 60^o with the magnetic field. The flux in maxwell through the coil is

If a particle is projected from point A, normal to the plane calculate

(i) Time of flight?

(ii) AB=?

Two particles $A$ and $B$ are moving with uniform velocity as shown in the figure given below at $t=0$.
Find out the shortest distance between the particles, if it occurs at $t=2.2\text{s}$

For a system of two particles of mass $2\text{kg}$ & $4\text{kg}$ lying on the same straight line. If mass $4\text{kg}$ is displaced rightwards by $5\text{m}$, then by what distance, $2\text{kg}$ must be moved to maintain the position of centre of mass of the system ?

Dimensional formula for force constant

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).

A police van moving on a highway with a speed of 30 km/h fires a bullet at a thief's car speeding away in the same direction with a speed of 192 km/h. If the nuzzle speed of the bullet is 150 m/s, with what speed does the bullet hit the thief's car?

The force between two small charged spheres having charges 3 × 10^-6C and 4 × 10^-6C placed 40 cm apart in air is

A mass of 0.3 Kg is attached to the end of a spring. If another mass of 0.04 Kg is added to the end of the spring, it stretches by 12 cm more. What would be the period of vibration of the system if 0.04 kg mass is removed?

A disc is rolling without slipping on a horizontal surface. $P$ and $Q$ are two points equidistant from $C$. Then, identify the correct statement regarding the velocity of the points:

A current of 1 A flows through the circular coil of radius 1cm as shown in the figure. Consider points A and B to be diametrically opposite. What will be the magnetic field at the center of the coil?

The coefficient of apparent expansion of a liquid in a copper vessel is C and in a silver vessel S. The coefficient of volume expansion of copper is ${\gamma }_C$. What is the coefficient of linear expansion of silver

A particle of mass 2 kg moves with an initial velocity of $(4\hat{i}+2\hat{j})m{s}^{-1}$ on the x-y plane. A force $\overrightarrow{F}=(2\hat{i}-8\hat{j})$ N acts on the particle. The initial position of the particle is (2 m,3 m). Then for y=3m,

If $\overrightarrow{a}=2\hat{i}+4\hat{j}+3\hat{k},\overrightarrow{b}=\hat{i}+2\hat{j}+\hat{k},$ then the scalar product and the angle between them are

If T is the surface tension of soap solution, the amount of work done in blowing a soap bubble from a diameter D to 2D is

A cart of mass $M$ moves with acceleration $a$ as shown in the figure. The minimum force required to hold a block of mass $m$ together is $($friction coefficient between two blocks is $\mu )$

For the potentiometer arrangement shown in the figure, length of wire AB is 100 cm and its resistance is $9\Omega$. Find the length of AC for which the galvanometer G will show zero deflection.

A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre of the cube at one end of the rod.Find the minimum possible flux of the electric field through the entire surface of the cube.

Two wires of the same material (Young's modulus $Y$) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $w$ is suspended from the combination as shown in the figure. The elastic potential energy stored in the system is

Two particles $A$ and $B$ move from rest along a straight line with constant accelerations $f$ and $h$ respectiely. If $A$ takes $m$ seconds more than $B$ and describes $n$ units more than that of $B$ acquiring the same speed, then

The density Of an ideal gas is 1.25 $\times {10}^{-3}$ g cm at STP. Calculate the molecular weight of the gas.

$Ify=A{e}^{mx}+B{e}^{nx},showthat\frac{d^{2}y}{d{x}^2}-(m+n)\frac{dy}{dx}+mny=0.$

Find the projection of the vector $\hat{i}+3\hat{j}+7\hat{k}$ on the vector $7\hat{i}-\hat{j}+8\hat{k}$

What is heavier on the surface of Earth: 1 m³ cotton or 1 m³ of Iron?{provided: ρ_iron>ρ_cotton}

A ball rolls off the top of stair way with a horizontal velocity of magnitude $1.8\text{m/s}$. The steps are $0.2\text{m}$ high and $0.2\text{m}$ wide. Which step will the ball hit first?

A stone is dropped from a height $h$. Another stone is thrown up simultaneously from the ground, which can reach to maximum height of $4h$. The two stones will cross each other after time

In a typical Indian Bugghi (a luxury cart drawn by horses),a wooden plate is fixed on the rear on which one person can sit.A bugghi of mass 200 kg is moving at a speed of 10 $km/h$.As it overtakes a school boy walking at a speed of 4 $km/h$,the boy sits on the wooden plate.If the mass of the boy is 25 kg,what will be the new velocity of the bugghi?

A man can row a boat $4km/hr$ in still water. He is crossing a river where the current is $2km/hr$. If the width of the river is $8km$, the time taken by him to cross with zero drift is

Consider the situation shown in figure. All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

The heights of mercury surfaces in the two arms of the manometer shown in figure (13-E1) are 2 cm and 8 cm. Atmospheric pressure = $1.01\times {10}^{5}N{m}^{-}2$. Find

(a) the pressure of the gas in the cylinder and

(b) the pressure of mercury at the bottom of the U tube.

A pendulum bob of mass 50 g is suspended from the ceiling of an elevator. Find the tension in the string if the elevator (a) goes up with acceleration 1.2 $m/s^2$, (b) goes up with deceleration 1.2 $m/s^2$, (c) goes up with uniform velocity , (d) goes down with acceleration 1.2 $m/s^2$, (e) goes down with deceleration 1.2 $m/s^2$ and (f) goes down with unifrom velocity.

In a stationary wave, all particles are

[MP PMT 1994]

A car is moving with a uniform acceleration of $4m/s^2$. What distance will it cover in 10 seconds after the start?

If the velocity time graph looks like this

Thief A is in an apartment 10m high and is throwing a bag of valuables horizontally at 5 m/s. Thief B is initially standing right below the point of release. Find the velocity with which he should run to catch the bag in time.

factors affecting Internal Resistance.

The ratio of acceleration due to gravity at a depth h below the surface of earth and at a height h above the surface of earth for h << radius of earth

Consider a gas with density $\rho$ and $\overline{c}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?

Length of the minute hand in a clock is $10\text{cm}$. Find difference between average speed and magnitude of average velocity (in $cm/min$) of tip of the minute hand from $6$ a.m. to $6:20$ a.m.

In $Cl{F}_3$, the lone pairs of electrons occupy equatorial positions to minimize

Two particles of mass 1 kg and 3 kg have position vectors $2\hat{i}+3\hat{j}+4\hat{k}and-2\hat{i}+3\hat{j}-4\hat{k}$ respectively. The centre of mass has a position vector

1) thermometer has its fixed points Marked as 5&95 what is the current temperature in degree centigrade when its thermometer reads 59 degree centigrade

2) In an orbital scale of thermometer water freezes at 40 degree centigrade and Boils at 290degree centigrade find its boiling point of liquid in Orbit scale if it boils at 62^O_C