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The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is

Three concetric spherical conductor A, B and C of radii R, 2R and 4R respectively. A and C is shorted and B is uniformly charged (charge +Q).

The potential at B is

In the figure a capacitor is filled with dielectrics. The resultant capacitance is:

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 ___ $(g=10m/s^2)$

In the arrangement, shown in figure, pulleys are massless and frictionless and threads are inextensible. Blocks of mass m1 will remain at rest if

Three points masses, each of mass m, are placed at the corners of an equilateral triangle of side l. Then the moment of inertia of this system about an axis along one of the side of the triangle is

If velocity v is given as v = a + bx + ct where a, b and c are constant and x and t are position and time, then which of the following is dimentionally correct?

A wire of length 2 mis made from $10c{m}^3$ of copper. A force Fis applied so that its length increases by 2 mm.Another wire of length 8 m is made from the same volume of copper. If the force is applied to it, its length will increase by

A disc is rolling on horizontal surface. If disc rolls without slipping, then the ratio of translational K.E. to total K.E. will be

Two geometrically identical cycle wheels of a bicycle moving due east have different number of spokes connected from center to rim. Rear wheel has $20$ spokes and the front wheel has only $10$ (the rim and the spokes have negligible resistance). A resistance $R$ is connected between center and rim in each wheel. The current in $R$ will be :

Two plane mirrors are placed perpendicular to each other and a point object $P$ is placed equidistant from both the mirrors. Find the equation of the geometerical shape at which the images of the object will lie.

Four condensers are joined as shown in Fig. The capacity of each is $8\mu F$. The equivalent capacity between the points A and B will be

A spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is:

Two parallel-plate capacitors, each of capacitance $40\mu F$, are connected in series. The space between the plates of one capacitor is filled with a dielectric of dielectric constant $K=3$, then the equivalent capacitance of the combination is

A vehicle can accelerate or decelerate at a maximum value of $1m{s}^{-2}$ and can attain a maximum speed of $20m{s}^{-1}$. If it starts from rest, what is the shortest time in which it can travel $1000m$, in a straight path, if it has to come to rest at the end of $1000m$?

A metallic chain with a length $\ell$ and whose ends are joined together is fitted onto a wooden disc as shown in the figure. The disc rotates with a speed of n revolutions per second. Then the tension of the chain T, if its mass is m, is

The body started with velocity of $8\text{m/s}$ and moving with an acceleration of $1{\text{m/s}}^2$. The distance travelled by the body in $6^{\text{th}}$ second is

A square loop of uniform conducting wire is as shown in figure. A
current-I (in amperes) enters the loop from one end and leaves the loop from opposite end as shown in figure. The length of one side of square loop is l metre. The wire has uniform cross section area and uniform linear mass density. In four situations of Column-I, the loop is subjected to four different uniform and constant magnetic field. Under the conditions of column I, match the column-I with corresponding results of column-II. ( $B_0$ in column I is a positive non-zero constant).



$\begin{array}{cc}ColumnI& ColumnII\\ \left(A\right)\overrightarrow{B}=B_0\hat{i}intelsa& \left(p\right)magnitudeofnetforceonloopis\sqrt{2}{B}_{0}Ilnewton\\ \left(B\right)\overrightarrow{B}=B_0\hat{i}intelsa& \left(Q\right)magnitudeofnetforceonloopiszero\\ \left(C\right)\overrightarrow{B}=B_0(\hat{i}+\hat{j})intesla& \left(R\right)magnitudeofnettorqueonloopaboutitscentreiszero\\ \left(D\right)\overrightarrow{B}=B_0\hat{k}intesla& \left(S\right)Netforceperpendiculartotheplaneofloop\end{array}$

A block of mass m is placed on a wedge. The wedge can accelerate in four manners marked as (1), (2), (3) and (4) as shown in the figure. If the normal reactions in situations (1), (2), (3) and (4) are $N_1,N_2,N_3$ and $N_4$ respectively, and acceleration with which the block slides down relative to the wedge in situations are $b_1,b_2,b_3$ and $b_4$ respectively and if $a<\frac{3g}{4},$ then

Find the projection of $\overrightarrow{A}=2\hat{i}-\hat{j}+\hat{k}$ along the vector $\overrightarrow{B}=\hat{i}+\hat{j}+\hat{k}$.

A stationary solid object weighing $3.5\text{kg}$ falls from a height of $2000\text{m}$ on a snow at $0^{\circ }\text{C}$. The object comes to rest immediately after collision. Then the amount of ice melted is
(Assume that all the energy of the ball is used in melting ice, latent heat of ice is $3.5\times 10{}^5\text{J/kg}$ and neglect air drag)

A uniform rod of length $L$ (in between the supports) and mass m is placed on two hinges A and B. The rod breaks suddenly at length $\frac{L}{10}$ from the support B. Find the reaction at hinge A immediately after the rod breaks :

A uniform rod of length $l=3\text{m}$ free to rotate in a vertical plane about a fixed horizontal axis passing through $O$. The rod is allowed to rotate by releasing from it's vertical position. Find the angular velocity of the rod when rod makes an angle $\theta ={60}^{\circ }$ with vertical. (take $g=10{\text{m/s}}^2$)

A man in a balloon, throws a stone downwards with a speed of $5\text{m/s}$ with respect to the balloon. The balloon is moving upwards with a constant acceleration of $5{\text{m/s}}^2.$ Then velocity of the stone relative to the man after $2\text{seconds}$ is:

All surfaces are smooth except that between $‘m^{\prime }$ and $‘2m^{\prime }$. The acceleration (in ${\text{m/s}}^2$) of the mass $‘m^{\prime }$ is

An RLC circuit with $R=100\omega$ is connected across ac source of 200V and angular frequency 300 rad/s. When only capacitance is removed, the current lags behind voltage by ${60}^{\circ }$. When only inductance is removed, the current leads the voltage by ${60}^{\circ }$. The current in the circuit is: (in Ampere)___

Block A is kept on top of block B and moves leftwards with respect to B. Assume the friction to be present between the blocks. The direction of friction force on A by B, will be?

The distance and displacement covered respectively by a particle after half a revolution of the circular path of radius $r$ are

Imagine a situation in which the given arrangement is placed inside an elevator that can move only in the vertical direction and compare the situation with the case when it is placed on the ground if the elevator accelerates downward with $a_o$(< g)

A rectangular loop of sides $10\text{cm}$ and $5\text{cm}$ with a cut, is stationary between the pole pieces of an electromagnet. The magnetic field of the magnet is normal to the loop. The current feeding the electromagnet is reduced so that the field decreases from its initial value of $0.3T$ at the rate of $0.02T{s}^{-1}$. If the cut is joined and the loop has a resistance of $2.0\Omega$, the power dissipated by the loop as heat is

A rectangular coil of 100 turns has length 5 cm and width 4 cm. It is placed with its plane parallel to a uniform magnetic field and a current of 2 A is sent through the coil. Find the magnitude of the magnetic field B, if the torque acting on the coil is $0.2N{m}^{-1}.$

In a rectangular park, a man walks $2$ km from south to north and then makes a ${160}^{\circ }$ turn to right and walks $2$ km more. He then again makes another ${160}^{\circ }$ turn to right and walks $2$ km more. If he continues this pattern until he reaches his starting point again, then the distance travelled by the man during this journey is
(correct answer + 2, wrong answer - 0.50)

A current loop of arbitrary shape lies in a uniform magnetic field B. Show that the net magnetic force acting on the loop is zero.

A solid body starts rotating about a stationary axis with an angular acceleration $alpha$ = $at$. How soon after the beginning of rotation will the total acceleration vector of an arbitrary point of the body form an angle = ${60}^{\circ }$ with its velocity vector?

Boyle’s law may be expressed as

In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at mid-point of screen with ${}^{\prime }{\mu }^{\prime }$ will be best represented by $\mu \ge 1$. [Assume slits of equal width and there is no absorption by slab]

What is the distance between two nodes called?

The energy of a photon of light of wavelength 450 nm is

A cylinder initially kept at rest on a horizontal rough surface is given an angular velocity $10\text{rad/s}$. What is the distance travelled by the centre of mass of the cylinder till it begins pure rolling ?
Given: Coefficient of kinetic and static frcition are equal $(\mu =0.5)$ and radius of cylinder $R=3\text{m}$. Also, take $g=10{\text{m/s}}^2$.

The average translational energy and the rms speed of molecules of a sample of oxygen gas at $300k$ are

$6.21\times {10}^{-21}J$ and $484m{s}^{-1}$ respectively. The corresponding values at $600K$ are nearly (assuming ideal

gas behavior)

Pressure inside two soap bubbles of a liquid solution are $1.01\text{atm}$ and $1.02\text{atm}$. Ratio of their volume is

A body starts from rest. What will be the ratio of the distance travelled by the body during the $4^{th}$ and $3^{rd}$ second?

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is/are

Calculate the acceleration of the block $B$ in the shown figure, assuming the surfaces and the pulleys $p_1$ and $p_2$ are smooth and the string is light.