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A transverse wave is described by the equation, $y=A\sin 2\pi (nt-\frac{x}{{\lambda }_0})$. The maximum particle velocity is equal to $3$ times the wave velocity, if

A wheel performs pure rolling on the ground. Find a point on the periphery of the body which has a velocity equal to the velocity of the centre of mass of the body.

A body of mass $0.01\text{kg}$ executes simple harmonic motion (SHM) about $x=0$ under the influence of a force as shown in figure. The time period of the SHM is :

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. Find the value of the triple product $\overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A})$.

In the arrangements shown in the figure below, block $A$ is connected to a spring and another block $B$ rests on $A$ and the system performs simple harmonic motion with a time period of $2\text{sec}$. The coefficient of static friction between $A$ and $B$ is $0.6$. The maximum amplitude of oscillation which the system can have, so that there is no relative motion between $A$ and $B$ is:

[Take $g=10{\text{m/s}}^2\&{\pi }^2\approx 10$]

In an orbital motion, the angular momentum vector is :

A block of mass $m$ is placed on a smooth inclined wedge ABC of inclination $\theta$ as shown in the figure. The wedge is given acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is

In the shown figure the tension in the horizontal cord is 30N. Find the weight of the body B.

A U-tube is partially filled with water. Oil, which does not mix with water, is next poured into one side, until water rises by 25 cm on the other side. If the density of the oil is 0.8 g/cc, the oil level will stand higher than the water level by

Two cylinders $A$ and $B$ having pistons contain equal amounts of an ideal diatomic gas at $300\text{K}$. The piston $A$ is free to move while the piston B is held fixed. Same quantity of heat is supplied to the gas in each cylinder. The temperature of the gas in cylinder $A$ rises by $35\text{K}$. The rise in temperature of the gas in cylinder $B$ is

A particle moving in a straight line has velocity and displacement equation as V = 4 $\sqrt{1+S}$ , where V in m/s and s is in m.

The initial velocity of the particle in m/s is ______

A wave, $y=2\text{sin}(\pi t+x+\frac{\pi }{6})$ is propagating on a stretched string fixed at one end. The equation of reflected wave can be given as

Find the acceleration of the block of mass $M$ in the situation shown in the figure. All the surfaces are frictionless and the pulley and the string are light.

One end of a copper rod of uniform cross section and length $1.5\text{m}$ is in contact with ice and the other end with steam at ${100}^{\circ }\text{C}$. At what point along its length from $\text{A}$ should a temperature of ${200}^{\circ }\text{C}$ be maintained so that in steady state, the mass of the ice melting is equal to that of steam produced in the same interval of time . $[L_v=540\text{cal/g},L_f=80\text{cal/ g}]$

A 2 kg mass moving with a velocity of $10m{s}^{-1}$ collides with another 6 kg mass moving in opposite direction with a velocity of $20m{s}^{-1}$. After the collision, they stick and move together. Find their common velocity and the momentum.

Point charges $Q_1=5mC$ (millicoulomb) and $Q_2=6mC$ (millicoulomb) are at a separation of 100m from each other. What is the magnitude of force on any one of the charge?

A gas has a density of $3\text{g/L}$ at S.T.P. What is its molar mass?

A ball is thrown up with initial velocity $u$. The retardation due to the drag is proportional to the velocity with proportionality constant, $\beta$. The maximum height and the time taken to reach the maximum height are

An object is moving in a straight-line path has a velocity of $40\text{m/s}$ at some instant. After $5\text{s}$, its velocity changed to $30\text{m/s}$. What is the average acceleration of the ball during this time interval?

For the masses and ideal-massless pulleys shown in figure find the ratio of magnitudes of accelerations of masses $A$ and $B$. Pulley $C$ is fixed to the ceiling and pulley $D$ is free to move vertically. All strings are inextensible and assume the string length to be equal between the pulley D and C and between the pulley D and the rigid support.

Hairs of shaving brush cling together when it is removed from water due to

What should be the pressure inside a air bubble of radius $0.1\text{mm}$ situated $1\text{m}$ below the water surface?

(Take surface tension of water $T=7.2\times {10}^{-2}\text{N/m}$ and $g=10{\text{m/s}}^2$)

In the figure shown, find the force exerted by the pulley at the support. Make necessary assumptions and take $g=10m/s^2$



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A solid body starts from rest. Angular acceleration of the body spinning about a stationary axis is given by $\alpha =2\cos \theta$ (in $rad/s^2$) where $\theta$ is the angle of rotation from initial position. Then which of the following graphs correctly represents the variation of angular velocity with respect to $\theta$?

Two cylinders of same cross-section and length $L$ but made of two different materials of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length $\frac{L}{2}$ above the surface of the liquid. If $d_1<d_2$ then

Three particles of masses $1\text{kg}$ , $2\text{kg}$ and $3\text{kg}$ are placed at the vertices $A,B,C$ respectively of an equilateral triangle $ABC$ of edge $1\text{m}$ as shown in the figure. Find the position of the centre of mass of the system. (If $A$ is assumed to be the origin).

If $S=ut+\frac{1}{2}a{t}^2$, where $S$ is displacement, $u$ is initial velocity (constant), $a$ is acceleration (constant) and $t$ is time taken, then differentiation of $S$ w.r.t. $t$ will be

The only force acting on a 2.0 kg body as it moves along the x - axis varies as shown in the figure. The velocity of the body at x = 0 is 4.0 $\frac{m}{s}$ What is the maximum K.E attained by the body between x=0 and x=5 m?

Light of frequency v is incident on a substance of threshold frequency $v_0(v_0<v)$. The energy of the emitted photo-electron will be

The equation $y=Asi{n}^2(kx-\omega t)$ represents a wave motion with

A sinusoidal wave represented by $y_i=0.3\cos (2x-40t)$ is travelling along a string towards a fixed end at $x=0$. Then, the equation of the reflected wave will be:-

(Assume there is no loss of energy at the boundary)

An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

Heat is supplied to an ideal monoatomic gas $A$ so that it expands without changing its temperature. In another process, starting with the same state, heat is supplied at constant pressure. In both the cases, a graph of work done by the gas

$\left(W\right)$ is plotted versus heat added $\left(Q\right)$ to the gas. The ratio of the slopes of the graphs obtained in the first and second processes is ${\eta }_1$. The same ratio obtained for an ideal diatomic gas is ${\eta }_2$ Find the ratio $\frac{{\eta }_1}{{\eta }_2}$.

A car going with constant speed on a circular path starts from point A at $t=0$ and reaches diametrically opposite point B after 2 sec then, it's angular velocity in rad/s is.

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. What is the angle betwee the two vectors?

A bus is moving with a velocity of 5 m/s towards a huge wall. the driver sounds a horn of frequency 165 Hz. If the speed of sound in air is 355 m/s, the number of beats heard per second by a passenger on the bus will be approximately,

If a ball is thrown vertically upwards with speed $u$, the distance covered during the last $t$ seconds of its ascent is

Minimum horizontal force $F$ required to keep the smaller block stationary with respect to the bigger block as shown in the figure is :

Three particles execute SHM along $x-$ direction with same frequency as $x_1=5\sin \omega t$, $x_2=5\sin (\omega t+{53}^{\circ })$, $x_3=-10\cos \omega t$. Find the amplitude of the resultant SHM.

If the resistance of a conductor is $5\Omega$ at ${50}^{\circ }C$ and $7\Omega$ at ${100}^{\circ }C$, then the mean temperature coefficient of resistance is

A chain of mass per unit length $\lambda =2\text{kg/m}$ is pulled up by a constant force $F$. Initially, the chain is lying on a rough surface and passes onto the smooth surface. The co-efficient of kinetic friction between chain and rough surface is $\mu =0.1$. The length of the chain is $L$. Then, find the speed ($\text{in m/s}$) of the chain when $x=L$. Take $g=10{\text{m/s}}^2$.

A block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in figure. The horizontal velocity of the block is:

A long string with a charge of $\lambda$ per unit length passes through an imaginary cube of edge $l$. The maximum possible flux of the electric field through the cube will be

Whenever a hydrogen atom emits a photon in the Balmer series

The masses and radii of the earth and moon are $M_1,R_{1}and{M}_2,R_2$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is

Two uniform rectangular plates having mass density ($\text{mass/area}$) $2{\text{kg/m}}^2$ and $1{\text{kg/m}}^2$ are joined together to form the $\text{L}$- shaped lamina as shown in the figure. Find the coordinates of centre of mass of the $\text{L}$-shaped lamina.

A thin disc of mass M and radius R has mass per unit area $\sigma \left(r\right)=k{r}^2$, where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is