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A block of mass $15\text{kg}$ is acted upon by a force $25\text{N}$ at an angle ${37}^{\circ }$ with the horizontal in a direction as shown in figure. The coefficient of static friction($\mu$) between the block and horizontal surface is $0.2$ . Find the frictional force acting on the block, so that it doesn't move. Take $(g=10{\text{m/s}}^2)$.

A ball is moving with an initial velocity $30\hat{i}\text{m/s}$ towards a wall oriented at an angle such that the velocity of the ball after collision with the wall becomes $-30\hat{j}\text{m/s}$. If mass of the ball is $0.5\text{kg}$, then the magnitude of the impulse imparted by the wall is

A rectangular film of liquid is extended from $(4\text{cm}\times 2\text{cm})$ to $(5\text{cm}\times 4\text{cm})$. If the work done is $3\times {10}^{-4}\text{J}$, then value of the surface tension of the liquid is

In photoelectric effect if the intensity of light is doubled then maximum kinetic energy of photoelectrons will

A swimmer can swim with a speed $v$ in still water





If the swimmer crosses a swimming pool of width ${}^{\prime }{d}^{\prime }$ from $A$ to directly opposite point $B$ on other side in time $t_1$ as shown in figure and in a flowing river (river velocity $u$) of same width ${}^{\prime }{d}^{\prime }$ from $A^{\prime }$ to directly opposite point $B^{\prime }$ on other bank in time $t_2$, then $\left(\frac{t_1}{t_2}\right)$ is equal to: (Assume $v>u$)

One end of a string of length $2\text{m}$ is tied to a body of mass $1\text{kg}$ and is whirled about the other end in a vertical circle at an angular speed of $4\text{rad/s}$. The tension in the string when the body is at the bottommost point of its motion will be equal to

Take $(g=10{\text{m/s}}^2)$

An ideal gas is expanded isothermally from a volume $V_1$ to volume

$V_2$ and then compressed adiabatically to original volume $V_1$. The initial pressure is $P_1$ and the final pressure iss $P_3$. If the net work done is W, then

At the instant the traffic light turns green, an automobile starts with a constant acceleration, $a=10m/s^2.$ At the same instant a truck, travelling with a constant speed of 5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be at that instant?

A uniform rod of length $l$ lies on a frictionless horizontal surface on which it is pivoted about its centre. A ball moving with speed $v$ as shown in figure collides with the rod at one of the ends. After hitting, the ball sticks to the rod. There is a similar uniform rod of length $l$, pivoted at one of its ends and a similar ball with same speed strikes the other end of the rod and sticks to it. The ratio of final angular momentum in both cases is:

A perfect gas goes from state $A$ to another state $B$ by absorbing $8\times {10}^5\text{J}$ of heat and doing $6.5\times {10}^5\text{J}$ of external work. The change in internal energy will be

On heating a uniform metallic cylinder, length increases by $3\%$. The area of cross - section of its base will increase by

For intensity I of a light of wavelength $5000\stackrel{\circ }{A}$ the photoelectron saturation current is 0.40 $\mu A$ and stopping potential is 1.36 V, the work function of metal is

A cubical block of side $0.5\text{m}$ floats on water with $30\%$ of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?

[Take density of water $={10}^3{\text{kg/m}}^3$]

In the circuit shown in figure neglecting source resistance, the voltmeter and ammeter readings will respectively be

A particle starts from rest and moving with an acceleration of $4{\text{ms}}^{–2}$ and covers a distance of $15\text{m}$. The final velocity of the particle will be

Ram and Satra are performing photo electric effect in the lab.

The number of electrons coming out from the emitter plate is same for both of them but in Ram's setup the electrons come out with velocity V while in Satra's setup they come out with 2V. Who will record a higher Photo current?

A point moves in a straight line so that its displacement $x$ at time $t$ is given by equation $x^2=t^2+1$. Its acceleration is:

In the Bohr's hydrogen atom model, the radius of the stationary orbit is directly proportional to (n = principle quantum number)

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 physical quantity $X$ is expressed as velocity $=\sqrt{\left(\frac{X}{\text{density}}\right)}$. The dimensions of $X$ are

In a Searle's experiment, the diameter of the wire as measured by a screw gauge with least count 0.001 cm is 0.050 cm. The length, measured by a scale of least count 0.1 cm, is 110.0 cm. When a weight of 50 N is suspended from the wire, the extension is measured to be 0.125 cm by a micrometer of least count 0.001 cm. Find the maximum error in the measurement of Young's modulus of the material of the wire from these data.

$y=\frac{W}{A}\times \frac{L}{X}$

Where W is the weight suspended from the wire, A is the cross section area, L is the length and X is the extension in the wire.



[IIT JEE 2004]

Two towns $\text{A}$ and $\text{B}$ are connected by a regular bus service with a bus leaving in either direction every $\text{T}\text{minutes}$. A man cycling with a speed $20\text{km/hr}$ in the direction $A$ to $B$ notices that a bus goes past him every $18\text{minutes}$ in the direction of his motion, and every $6\text{minutes}$ in the opposite direction. What is the period $T$ of the bus service and with what speed do the buses ply on the road. Assume the buses ply with constant speed on the road.

A particle is projected with a velocity of $\sqrt{7}m{s}^{-1}$ at an angle ${60}^{\circ }$ with horizontal. Find the average velocity of the projectile between the instants of point of projection and reaching the highest point

There are four solid balls with their centres at the four corners of a square of side $a$. The mass of each sphere is $m$ and radius $r$. Find the moment of inertia of the system about one of the sides of the square.

A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the pulley is

The position vector of a projectile is given by $\overrightarrow{r}=3t\hat{i}+(4t-5t^2)\hat{j}$. Find the ratio of maximum height and initial speed.

($g=10{\text{m/s}}^2$)

The temperatures of equal masses of three different liquids $A,B$ and $C$ are ${12}^{\circ }\text{C},{19}^{\circ }\text{C}$ and ${28}^{\circ }\text{C}$ respectively. The temperature when $A$ and $B$ are mixed is ${16}^{\circ }\text{C}$, when $B$ and $C$ are mixed is ${23}^{\circ }\text{C}$. What is the temperature when $A$ and $C$ are mixed?

A tuning fork vibrating with a sonometer in fundamental mode having a wire of length $20\text{cm}$ produces $5$ beats per second. The beat frequency does not change if the length of the wire is changed to $21\text{cm}$. The frequency of the tuning fork is

A moving particle of mass 'm' makes a head-on collision with a particle of mass '2m' initially at rest. If the collision is perfectly elastic, the percentage loss of energy of the colliding particle is

Two vertical plane mirrors are inclined at an angle of ${60}^{\circ }$ with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

A large horizontal surface is in $SHM$ with an amplitude of $1\text{cm}$. A mass of $10\text{kg}$ is kept gently on it when it is at mean position. For the mass to always remain in contact with the surface, the maximum frequency of $SHM$ will be

In which quadrant does the point $(-3,4)$ lie?

A body has an initial velocity of 25 m/s in the negative x-direction. The following figure represents it's a - t graph. Find its displacement at t = 15s.

Radius of gyration of a uniform disc about a line perpendicular to the plane of disc is equal to its radius $R$. If the distance of the line from the center is $\frac{R}{\sqrt{x}},$ find the value of $x$.

If the work function of a photometal is 6.825 eV. Its threshold wavelength will be $(c=3\times {10}^{8}m/s)$

If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is

A disc of radius $0.1\text{m}$ rolls without sliding on a horizontal surface with a velocity of $6\text{m/s}$. It then ascends a smooth continuous track as shown in figure. The height upto which it will ascend is $(g=10{\text{m/s}}^2)$.

A block of ice at $-{10}^{o}C$ is slowly heated and converted to steam at ${100}^{o}C.$ Which of the following curves represents the phenomenon qualitatively?

A point charge Q is placed just outside a cube of side 'a' near corner H. Flux of electric field associated with face ABCD is

A bullet leaving the muzzle of a rifle barrel with a velocity $v$ penetrates a plank and loses ${\frac{1}{5}}^{th}$ of its velocity. It then strikes the second plank, which it just penetrates through. Find out the ratio of the thickness of the planks. [Supposing the average resistance to the penetration is the same in both the case]

An $F-x$ graph is shown below. Find the difference in initial and final potential energies from $x=0\text{m}$ to $x=3\text{m}$.

A slab of glass of thickness of $3$ units and refractive index $\sqrt{3}$ is surrounded by vacuum and is placed as shown. A light ray is incident at the point $(2,5\sqrt{3})$ as shown. The point where the ray will cut the $X-$ axis is:

There is a uniform magnetic field $B$ directed in negative $z$ direction. A conductor $ABC$ has length $AB=l_1$, parallel to the $x-$axis, and length $BC=l_2$ parallel to the $y-$axis. $ABC$ moves in the $xy$ plane with velocity $v_x\hat{i}+v_y\hat{j}$. The potential difference between $A$ and $C$ is proportional to

A car moving on a straight road covers one third of the distance with 20 km/hr and the rest with 60 km/hr. The average speed is

The smallest division on the main scale of a Vernier callipers is $1\text{mm}$ and 10 vernier divisions coincide with 9 main scale divisions. While measuring the diameter of a ring, the zero mark of the vernier scale lies between $5.0\text{cm}$ and $5.1\text{cm}$ and the eighth division of the vernier scale coincides with a main scale division. The diameter of the ring is :

At what temperature is the velocity of sound double than that at $0^{\circ }C$?

If $\overrightarrow{A}$ is parallel to$\overrightarrow{B}$ then choose incorrect option $\left(\lambda \text{is positve constant}\right)$

The thermal capacity of $100\text{g}$ of aluminum (specific heat $=0.2{\text{cal/g}}^{\circ }\text{C})$ is

The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

Which of the following gases can be most easily liquified? Given, the value of $a$ in van der Waals equation for $N{H}_3=4.17,C{O}_2=3.59,S{O}_2=6.71\&C{l}_2=6.49$