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For small applied force, the slope of graph between friction and applied force is

A two particle system with masses $2\text{kg}$ and $3\text{kg}$ are present at (15,0) and (0, 20) in a $x,y$ plane. Then its centre of mass lies on lines

If the flux of magnetic induction through a coil of resistance R and having n turns changes from ${\Phi }_1$ to ${\Phi }_2$, then the magnitude of the charge that passes through the coil is

A force of $5\text{N}$, making an angle $\theta$ with the horizontal, acting on an object and displaces it by $0.4\text{m}$ along the horizontal direction. If the work done by the force is $1\text{J}$, then the horizontal component of the force is

The neutron was discovered by

A wire-loop confined in a plane is roated in its own plane with some angular velocity. A uniform magn etic field exists in the region. Find the emf induced in the loop.

An infinite thread of charge density $\lambda$ lies along z-axis. The potential difference between points A(4, 3, 4) and B(3, 4, 0) is

Give
the resonating structures of NO₂
and N₂O₅.

When a current of $5mA$ is passed through a galvanometer having a coil of resistance $15\Omega$, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range $0-10V$ is

A 2.00 m-long rope, having a mass of 80 g, is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N. Find the frequencies of the fundamental and the first two overtones.

A semi-circular rigid wire of radius R carrying current I is placed inside external uniform magnetic field of magnitude B as shown. Net magnetic force on the wire is



I धारा ग्रहण किए हुए R त्रिज्या के एक अर्द्ध-वृत्तीय दृढ़ तार को दर्शाए अनुसार B परिमाण के बाह्य एकसमान चुम्बकीय क्षेत्र के अन्दर रखा जाता है। तार पर नेट चुम्बकीय बल है

A small ball of mass $m$ collide with a smooth wall, moving with constant speed $u$ at an angle $\theta$ with the normal to the wall. After collision, the ball moves at the same angle $\theta$ with the normal to the wall with the same constant speed. Find the average impulse on the ball.

A person of mass $60\text{kg}$ is inside a lift of mass $940\text{kg}$ and presses the button on control panel. The lift starts moving upwards with an acceleration $1.0{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, the tension in the supporting cable is

An Express train moving at 30 metre per second produces its feet to 10 M per second in a distance of 240 M. If the breaking falls is increased by 12.5% in the beginning.find the distance it travels before coming to rest

If the two terminals of a battery of $40\text{V}$ are connected across $\text{A}$ and $\text{B}$, the charge flown through the battery will be



Given: $C_1=5\mu F,C_2=2.5\mu F,C_3=6\mu F,C_4=2\mu F$ and $C_5=15\mu F$

A wheel of radius $20\text{cm}$ has four forces applied to it, as shown in the figure. The total torque produced by these forces about centre $O$ is

An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho )$

Two stones are thrown vertically upwards simultaneously with their initial velocities $u_1$ and $u_2$ respectively. Prove that the heights reached by them would be in the ration of $u_1^2$ ; $u_2^2$ ( Assume upward acceleration is –g and downward acceleration to be +g).

Both the strings, shown in figure, are made of same material and have same cross-section. The pulleys are light. The wave speed of a transverse wave in the string $AB$ is $v_1$ and in $CD$ it is $v_2$. Then $\frac{v_1}{v_2}$ is

An inductor $L=20\text{mH}$, a resistor $R=100\Omega$ and a battery $E=10\text{V}$ are connected in series. After a long time the battery is short-circuited. Find the current in the circuit, $1\text{ms}$ after short-circuiting.

$[$Use $e^{-5}=0.00673]$

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 ?

A microphone of cross-sectional area 0.80 $c{m}^2$ is placed in front of a small speaker emitting 3.0 W of sound output. If the distance between the microphone and the speaker is 2.0 m, how much energy falls on the microphone in 5.0 s?

A block of mass $1\text{kg}$ is at rest relative to a smooth wedge moving leftwards with constant acceleration $a=5{\text{ms}}^{-2}.$ Let $N$ be the normal reaction between the block and the wedge. Take $g=10{\text{ms}}^{-2}$. Choose the correct options from the choices given below:

A stone of mass m is attached to one end of a wire of cross-sectional area A and young's modulus Y. The stone is revolved in a horizontal circle at a speed such that the wire makes an angle $\theta$ with the vertical. The strain produced in the wire will be,

An iron rod and another of brass, both at ${27}^{\circ }C$ differ in length by ${10}^{-3}m$. The coefficient of linear expansion for iron is $1.1\times {10}^{-5}$${/}^{\circ }C$ and for brass is $1.9\times 10-5$${/}^{\circ }C$. The temperature at which both these rods will have the same length is

Silver has a work function of $4.7\text{eV}$. When ultraviolet light of wavelength $100\text{nm}$ is incident upon it, a potential of $7.7\text{V}$ is required to stop the photoelectrons from reaching the collector plate. How much potential will be required to stop the photoelectrons when light of wavelength $200\text{nm}$ is incident upon silver?

1. 12

The vernier scale used for measurement has a positive zero error of $0.2\text{mm}$. If while taking a measurement it was noted that $0$ on the vernier scale lies between $8.5\text{cm}$ and $8.6\text{cm}$, vernier coincidence is $6$, then the correct value of measurement is ________$\text{cm}$.



$($Least count $=0.01\text{cm})$

Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of M to that of N is-

The total work done by three forces on a block is $60\text{J}$. If block is displaced by a force from position $A(1,2,3)$ to $B(7,6,5)$. Find out the third force if the other two forces are $\overrightarrow{F_1}=(7\hat{i}+3\hat{j}+2\hat{k})\text{N}$, and $\overrightarrow{F_2}=(-2\hat{i}+2\hat{j}+\hat{k})\text{N}$.

Assume that $\overrightarrow{F_3}$ is perpendicular to $XY$ plane.

The frequency and work function of an incident photon are v and ${\varphi }_0$. If $v_0$ is the threshold frequency then necessary condition for the emission of photo electron is

In the figure shown, the cart of mass $6m$ is initially at rest. A particle of mass $m$ is attached to the end of the light rod which can rotate freely about A. If the rod is released from rest in a horizontal position shown, determine the velocity $v_{rel}$ of the particle with respect to the cart when the rod is vertical, then

Two blocks were held against a frictionless wall and released, the surfaces between the block have friction. If mass of A is less than mass of B, then which of the following is correct

Why do birds fly off a high tension wire when the current is switched on?

Two Carnot heat engines are put in series such that heat rejected by one engine is used in the second engine as heat input. If efficiency of first engine is $30\text{\%}$, and overall combination has efficiency of $65\text{\%}$, then the efficiency of second engine is