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Two blocks of masses 10 kg and 20 kg are placed on the X-axis.The first mass is moved on the axis by a distance of 2 cm.By what distance should the second mass be moved to keep the position of the centre of mass unchanged?

A particle moves with a velocity $\overrightarrow{v}=5\hat{i}-3\hat{j}+6\hat{k}m{s}^{-1}$ under the influence of a constant force $\overrightarrow{F}=10\hat{i}+10\hat{j}+20\hat{k}N$ . The instantaneous power applied to the particle is

A point traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for one-third of the remaining time and with velocity $v_2$ for the remaining time. The mean velocity of the point averaged over the whole time of motion

Suppose $\overrightarrow{a}$ is a vector of magnitude 4.5 unit due north. What is the vector (a) 3 $\overrightarrow{a}$, (b) -4 $\overrightarrow{a}$ ?

A water jet is being used to fill a cylindrical container of diameter $1m$ and height $2m$. The jet shoots the water at an angle of ${45}^o$ with velocity $u$ above the same horizontal plane on which the container is kept. The distance between the jet and container is $6m$ as shown in the diagram. For which of the following value(s) of $u$, the water will fill up the container. (Take $g=10m/s^2)$

A block of mass $m$ is attached rigidly with a light spring of force constant $k$. The other end of the spring is fixed to a wall. If block is displaced by a distance $x$, find the work done on the block by the spring for this range. (The spring force is given by $F=-kx$ , where $k$ is spring constant and $x$ is displacement of the block.)

A particle is subjected to two simple harmonic motions given by

$x_1=2.0sin\left(100\pi t\right)$ and $x_2=2.0sin(120\pi t+\frac{\pi }{3})$,

where x is in centimeter and t in second. Find the displacement of the particle at

(a) t = 0.0125,

(b) t = 0.025

When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.

A force is equal to $85.75\text{dyne}$. If it is expressed in $\text{Newton}$, then the number of significant figures will be

What is photoelectric threshold frequency?

A particle of charge per unit mass $\alpha$ is released from origin with velocity $\overrightarrow{v}=v_0\hat{i}$ in a magnetic field $\overrightarrow{B}=-B_0\hat{k}$
for $x\le \frac{\sqrt{3}}{2}\frac{v_0}{B_0\alpha }$,
And $\overrightarrow{B}=0forx>\frac{\sqrt{3}}{2}\frac{v_0}{B_0\alpha }$,
The x co-ordinate of the particle at time $t(>\frac{\pi }{3B_0\alpha })$

Two identical conducting very large plates having charges +4Q and +6Q are placed close to each other at separation d. The plate area of either face of the plate is A. The potential difference between plates $P_1$ and $P_2$ is

Two strings are attached to each other as shown in the figure. The linear mass density of the second string is four times that of the first string and the boundary between the two strings is at $x=0$. The wave equation of the incident wave at the boundary is $y_i=A_i\cos (k_{1}x-{\omega }_{1}t)$. Then, which of the following correctly represents the equation of the transmitted wave? Assume, tension in the two strings are same.

What is the power required by the pump to lift $1000\text{kg}$ of water per minute from a $20\text{m}$ deep well and eject it with the speed of $20\text{m/s}$?

A strip of wood of mass $M$ and length $l$ is placed on a smooth horizontal surface. An insect of mass $m$ starts at one end of the strip and walks to the other end in time $t$, moving with constant speed. The speed of the insect as seen from the ground is

A particle of mass m and charge q, moving with velocity v enters region II normal to the boundary as shown in the following figure. Region II has a uniform magnetic field B. Choose the correct choice(s).

A particle exhibits linear simple harmonic motion with an amplitude of $3cm$. When the particle is at $2cm$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Its time period in seconds is

In the given figure $V_B$ is (All surfaces are smooth and string is massless and inextensible)

A block of mass 'm' is supported on a rough wall by applying a force P as shown in figure. Coefficient of static friction between block and wall is ${\mu }_s$

For what range of values of P, the block remains in static equilibrium?

On a smooth inclined plane, a body of mass M is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant K, the period of oscillation of the body (assuming the springs as massless) is

In an experiment on photoelectric effect, the emitter and the collector plates are placed at a separation of 10 $cm$ and are connected through an ammeter without any cell.

A magnetic field $B$ exist parallel to the plates. The work function of the emitter is 2.39 $eV$ and the light incident on it has wavelengths between 400 $nm$ and 600 $nm$ . Find the minimum value of $B$ for which the current registered by the ammeter is zero. Neglect any effect of space charge.

A solid sphere of mass $500\text{g}$ and radius $10\text{cm}$ rolls without slipping with a velocity of $20\text{cm/s}$. The total $K.E$. of the sphere is nearly

One nanometer is equal to

At t = 0, light of intensity $\frac{{10}^{12}photons}{s{m}^2}$ of energy 6eV per photon start falling on a plate with work function 2.5 eV. If area of the plate is $2\times {10}^{-4}{m}^2$ and for every ${10}^5$ photons one photoelectron is emitted, charge on the plate at t = 25 s is

A solid cylinder of mass $m$ is kept on the edge of a plank of mass $3m$ and length $15\text{m}$ which in turn is kept on smooth ground. The coefficient of friction between the plank and the cylinder is $0.1$. The cylinder is given an impulse which imparts it a velocity of $6\text{m/s}$ but no angular velocity. Find the time after which the cylinder will start pure rolling.

What is the angular momentum of an electron in Bohr’s hydrogen atom whose energy is - 0.544 eV.

A $5\text{kg}$ block slides down an inclined plane, having angle of inclination ${30}^{\circ }$ from horizontal. Find the acceleration (${\text{m/s}}^2$) of block, if the coefficient of kinetic friction is ${\mu }_k=\frac{1}{2\sqrt{3}}$. Take $g=10{\text{m/s}}^2$ .

Find the difference in the height of the liquid between the centre and the edge $\left(\text{in cm}\right)$, if the fluid is rotated in a container as shown in figure.
[Take ${\pi }^2=10,g=10{\text{m/s}}^2$]

A boy covers a distance $AB$ of $2\text{km}$ with speed of $2.5\text{km/hr}$, while going from $A$ to $B$ and comes back from $B$ to $A$ with speed $0.5\text{km/hr}$, his average speed will be

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.

Find velocity of block $B$ at the instant shown in figure. Assume the surface and pulleys to be frictionless and string to be inextensible.

With what minimum acceleration can a fireman slide down a rope whose breaking strength is $\frac{2}{3}$ of his weight?
(Hint:-Use the concept of pseudo-force.)

The area of cross section of a steel wire of Young's modulus $Y=2.0\times {10}^{11}{\text{N/m}}^2$ is $0.1{\text{cm}}^2$. Find the force required to double its length.
(Assume area of cross section remains same)

No work is done by a force on an object if

a) force is always perpendicular to its velocity

b) the object is stationary but the point of application of force moves on the object

c) the object moves in such a way that the point of application Of the force also moves

d) the force is always perpendicular to its acceleration.

A ball dropped from a point $A$ falls down vertically to $C$, through the midpoint $B$. The descending time from $A$ to $B$ and that from $A$ to $C$ are in the ratio

A ball is released from the top of a tower. The ratio of work done by force of gravity in $1^{st}$ second, $2^{nd}$ second and $3^{rd}$ second of the motion of ball is

A plane simple harmonic progressive wave given by the equation, $y=A\sin (\omega t-kx)$ of wavelength $120\text{cm}$ is incident normally on a plane surface which is a perfect reflector (acts as fixed end). If a stationary wave is formed, then the ratio of amplitudes of vibrations at points $10\text{cm}$ and $30\text{cm}$ from the reflector is

(Here $x$ is measured from reflector)

A block is gently placed on a conveyor belt moving horizontally at a constant speed. After $t=4\text{s}$, the velocity of the block becomes equal to the velocity of the belt. If the coefficient of static friction between the block and the belt is $\mu =0.2$, then what is the velocity of the conveyor belt ?

A sample of an ideal gas has diatomic molecules at a temperature at which effective degree of freedom is $5$. Under the action of radiation, each molecule splits into two atoms. If the ratio of the number of dissociated molecules to the total number of molecules is $\alpha$, then find the ratio of molar specific heat capacities $(\gamma =\frac{C_P}{C_V})$.

If a boat can go with a maximum velocity of 40 km/hr with respect to water in a pond, then what will be the boat's maximum velocity with respect to water in a river flowing at 20 km/hr.

(i) upstream (ii) downstream respectively.

The temperature coefficient of resistance of a wire is 0.00125 per °C. At 300 K, its resistance is 1 ohm. This resistance of the wire will be 2 ohm at
(IIT-JEE 1980)

If one face of a prism of angle ${30}^{\circ }$ and refractive index $\mu =\sqrt{2}$ is silvered, the incident ray retraces its initial path. The angle of incidence is