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A chain of length $L=10\text{m}$ and mass $m=20\text{kg}$ is allowed to fall on a table such that the part falling on the table comes to rest immediately. The force acting on the table when $5\text{m}$ of it has fallen on the table is [Take $g=10{\text{m/s}}^2$]

Two circular coils $X$ and $Y$, having equal number of turns and carrying equal currents in the same sense, subtend same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$ and if we represent the magnetic field due to bigger coil $Y$ at $O$ as $B_y$ and that due to smaller coil $X$ at $O$ as $B_x$, then

Calculate Reynold’s number, if a fluid having a viscosity of $0.4{\text{Ns/m}}^2$ and density of $900{\text{kg/m}}^3$ flows through a pipe of length $20\text{mm}$ with a velocity of $2.5\text{m/s}$.

The equation of a progressive wave is $y=0.02sin2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$ here x and y are in metres and t is in seconds. The velocity of propagation of the wave is

Two resistors of resistance $R_1$and $R_2$having $R_1>R_2$ are connected in parallel. For equivalent resistance R, the correct statement is

The retarding acceleration of $7.35m/s^2$ due to frictioanl forcer stops the car of mass $400kg$ travelling on road. The coefficient of friction between the tyre of the car and the road is

A long wire carrying a current of 20A is fixed. Another long wire AB is to be balanced mid-air a distance 2cm. Find the magnitude of the current in AB. Also find the angular frequency of SHM. If AB is slightly disturbed from this position. Given the mass per unit length of the wires is ${10}^{-6}kg/m$

A particle of specific charge $\alpha$ starts moving from the origin under the action of an electric field $\overrightarrow{E}=E_0\hat{i}$ and magnetic field $\overrightarrow{B}=B_0\hat{k}$. Its velocity at $(x_0,y_0,0)$ is $(4\hat{i}+3\hat{j})$. The value of $x_0$ is

Fusion reaction is initiated with the help of

The length of cylinder is measured with a metre rod having least count $0.1\text{cm}$. Its diameter is measured with vernier caliper having least count $0.01\text{cm}$. Given that length is $5.0\text{cm}$ and diameter is $4.0\text{cm}$. The percentage error in the calculated value of the volume will be

In a fission reaction

${}_{92}^{238}U\to {}^{117}X{+}^{117}Y+n+n$

the binding energy per nucleon of X and Y is 8.5 MeV whereas that of ${}^{236}U$ is 7.6 MeV. The total energy liberated will be about

A man running on a circular track of radius$=20\text{m}$, Find the linear distance travelled by the man when he completes $5$ revolutions?

Angle of glass prism is ${60}^{\circ }$ and refractive index of the material of the prism is 1.414,then what will be the angle of incidence, so that ray should pass symmetrically through prism

A large open tank has two holes in the wall. One is a square hole of side $2\text{cm}$ at a depth of $5\text{cm}$ from the top and the other is a circular hole of radius $R$ at a depth of $20\text{cm}$ from the top. When the tank is completely filled with water, the quantity of water flowing out per second from both the holes is same. Then, what is the value of $R$?

A tuning fork producing sound of frequency $380\text{Hz}$ is moving towards a wall with a velocity of $4{\text{ms}}^{-1}$. The number of beats per second heard by a stationary listener produced due to direct and reflected sounds will be

[speed of sound in air $=340{\text{ms}}^{-1}$]

Two transverse waves in a given medium are represented by the curve as shown in the figure. Find the ratio of their intensities. All the measurements are in $\text{S.I}$ units.

X-rays are not used for radar purpose because

Two metal rods $1$ and $2$ of same lengths have the same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$, and cross-sectional areas $A_1$ and $A_2$ respectively. If the rate of heat conduction in $1$ is four times that in $2$, then

100 mA current gives a full-scale deflection in a galvanometer of $2\Omega$ . The resistance connected with the galvanometer to convert it into a voltmeter to measure $5V$ is

A small ring $P$ is threaded on a smooth wire bent in the form of a circle of radius $a$ and center $O$. The wire is rotating with constant angular speed $\omega$ about a vertical diameter $xy$, while the ring remains at rest relative to the wire at a distance $\frac{a}{2}$ from $xy$. Then ${\omega }^2$ is equal to

A car accelerates uniformly from $20{\text{ms}}^{–1}$ to $50{\text{ms}}^{–1}$ while entering the motorway, covering a distance of $200\text{m}$. Then the acceleration of the car will be:

A block is placed on the top of a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation $a$, the block is released. The acceleration of the block relative to the incline is

A man is sitting on the shore of a river. He is in the line of a 1.0 m long boat and is 5.5 m away from the center of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of Projection and the edge of the boat are in the same horizontal level.

In a certain double slit experimental arrangement interference fringes of width 1.0 mm each are observed when light of wavelength 5000 Å is used. Keeping the set up unaltered, if the source is replaced by another source of wavelength 6000 Å, the fringe width will be

[CPMT 1988]

A particle travels along the x-axis. Its velocity time graph is shown above.

What is the total displacement of the particle at t = 20 sec?

Figure shows a vertical cylindrical vessel separated in two parts by a frictionless piston free to move along the length of the vessel. The length of the cylinder is 90 cm and the piston divides the cylinder in the ratio of 5:4. Each of the two parts of the vessel contains 0.1 mole of an ideal gas. The temperature of the gas is 300 K in each part. Calculate the mass of the piston

Which of the following represents the correct dimensions of the gravitational constant?

Two light springs of force constant $K_1$ and $K_2$ and a block of mass $m$ are arranged in one line $AB$ on a smooth horizontal table such that one end of each spring is fixed on rigid supports and the other end is free as shown in the figure. The distance $CD$ between the free ends of the spring is $60\text{cm}$. If the block moves along $AB$ with a velocity $120\text{cm/s}$ in between the springs, calculate the period of oscillation of the block.

(Assume that the dimensions of the cube is much less than $60\text{cm}$)

$(K_1=1.8\text{N/m},K_2=3.2\text{N/m},m=200\text{gm})$

A bike experiences a total reaction force of $1000\text{N}$ when it tilts through an angle of ${60}^{\circ }$ with the vertical, while moving with a velocity of $15\text{m/s}$ on a frictionless road with a radius of curvature of $25\text{m}$. What is the mass of the bike? $(g=10{\text{m/s}}^2)$

A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction

Wave is associated with matter

Evaluate: $\int \left(\cos \right(x)-\frac{3}{x^5})dx$

A metallic block carrying current I is subjected to a uniform magnetic field $\overrightarrow{B}$ as shown in the figure. The moving charges experience a force $\overrightarrow{F}$ given by ........... which results in the lowering of the potential of the face ........ Assume the speed of the carriers to be v

A projectile of mass 50 kg is projected vertically upward with a velocity of 100 m/s. After 5 seconds it explodes into two pieces, one piece of 20 kg moving vertically upward with a velocity of 150 m/s. The algebraic sum of the momentum of the system 3 seconds later is

The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta \left(t\right)=2t^3-6t^2$. The torque on the wheel becomes zero at

A particle '$m$' starts with zero velocity along a line $y$ = $4d$. (Where $d$ is a constant). The position of particle '$m$' varies as $x$ = $Asin\omega t$. At $\omega t$ = $\frac{\pi }{2}$, its angular momentum with respect to the origin is?

The vertical height of the projectile at time $t$ is given by $y=4t-5t^2$ and the horizontal distance covered is given by $x=3t$ where $x$ and $y$ are in $\text{m}$ and $t$ in $\text{s}$. What is the angle of projection with the horizontal?

Two forces $\overrightarrow{F_1}=(2\hat{i}+2\hat{j})N$ and $\overrightarrow{F_2}=(3\hat{j}+4\hat{k})N$ are acting on a particle. The component of force $\overrightarrow{F_1}$ along force $\overrightarrow{F_2}$ is

The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y=(8t-5t^2)$ meter and x = 6t meter, where t is in second. The velocity with which the projectile is projected is

A bike can travel at maximum of 100 km/hr on ground. A train is travelling at the rate of 100 km/hr. If i put the bike on the train then what could be the maximum and minimum velocity that the bike can be seen to go with respect to a person on the ground?

The potential energy $U$ of a particle of mass $m=1\text{kg}$ moving in $x-y$ plane is given by $U=3x+4y,$ where $x$ and $y$ are in metre and $U$ is in joule. If initially particle was at rest, then its speed at $t=2\text{s}$ will be

In the diagram below, Ram holds the rod with force $F$. Column II of the table gives the readings shown by the weighing machine $\left(\text{W.M.}\right)$ for various values of $F$ given in Column-I. Then choose the correct matching. (All forces are in newtons)

A $95kg$ halfback (HB) makes a turn on the foot ball field. The half back sweeps out a path that is a portion of a circle with a radius of $12m$ The halfback makes a quarter turn on a circular path in $2.1$ seconds. The net force acting on the half back will be:

The work done in increasing the length of a $1\text{m}$ long wire of cross-sectional area $1{\text{mm}}^2$ through $1\text{mm}$ will be

[Given, $Y=2\times {10}^{11}{\text{N/m}}^2$]

The x and y co-ordinates of a particle at any time ‘t’ are given by x = 2t + 5t² and y = 7t, where x and y are in metre and t is in second. Velocity of the particle at t = 2 s will be



किसी समय t पर एक कण के x तथा y निर्देशांकों को x = 2t + 5t² तथा y = 7t द्वारा व्यक्त किया जाता है, जहाँ x तथा y मीटर में हैं तथा t सेकण्ड में है। t = 2 s पर कण का वेग होगा

A spherical ball of radius $5\text{mm}$ flowing through the glycerin as shown in figure. The velocity of ball at a particular instant is $0.6\text{m/s}$. Find the drag force on the ball due to the fluid. Assume that Stoke's law is valid. (Take viscosity of glycerine as $0.950\text{kg/m-s}$)