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A nucleus ruptures into two nuclear parts which
have their velocity ratio equal to 2:1, then what is the ratio of their nuclear
size?

A $200\text{Hz}$ sinusoidal wave is travelling in the positive x-direction along a string with a linear mass density of $4\times {10}^{-3}\text{kg/m}$ and a tension of $40\text{N}$. At time $t=0$, the point $x=0$ has maximum displacement in the positive y-direction. Next when this point has zero displacement, the slope of the string is $\pi /20$. Which of the following expressions represents the displacement of string as a function of $x$ (in metres) and $t$ (in seconds)?

Charges + q and -q are. placed at the vertices B and C of an isosceles triangle the potential at vertex A is

Two bodies are projected simultaneously with the same velocity of 19.6 m/s from the top of a tower , one vertically upwards and the other vertically downwards. As they reach the ground, the time gap is

A pulse moving along $x-$axis is represented by the wave function $y(x,t)=\frac{2}{(x-2t{)}^2+1}$ where $x$ and $y$ measured in centimeters and $t$ is measured in seconds. The shape of pulse $y(x,0)=\frac{2}{x^2+1}$ is shown in the figure below. Which of the following correctly represents the shape of pulse at $t=1\text{s}$.

Find the force exerted by $3\text{kg}$ body on $1\text{kg}$ assuming all surfaces are smooth ($g=10{\text{m/s}}^2$)

What would be the work done by the gas if the entire process is reversed (3 - 2 - 1)?

The field lines for single positive charge are:

Two capillary tubes of same radius r but of lengths $l_1$ and $l_2$ are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the length of a single tube that can replace the two tubes so that the rate of flow is same as before

Given below are some functions of x and t to
represent the displacement (transverse or longitudinal) of an elastic
wave. State which of these represent (i) a traveling wave, (ii) a
stationary wave or (iii) none at all:

(a) y = 2 cos (3x) sin (10t)

(b)

(c) y = 3 sin (5x – 0.5t) + 4 cos (5x
– 0.5t)

(d) y = cos x sin t + cos 2x sin 2t

Interference fringes are observed on a screen by illuminating two thin slits $1\text{mm}$ apart with a light source $(\lambda =632.8\text{nm})$. The distance between the screen and the slits is $100\text{cm}$. If a bright fringe is observed on a screen at a distance of $1.27\text{mm}$ from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits, is close to :

Shunt capacitors are used to raise the power factor of the load of 100 kW from 0.8 lagging to unity. The supply is 3-$\varphi$, 50 Hz, 10 kV. If star capacitor bank is used, then the capacitance per phase required will be

A particle of mass $1kg$ is projected with a velocity of $20m/s$ at an angle of ${30}^{\circ }$ with the horizontal. Find the change in the momentum $(kg-m/s)$ of the particle between the points of projection and the highest point. Take $g=10m/s^2$

A liquid having mass $m=250\text{g}$ is kept warm in a vessel by using an electric heater. The liquid is maintained at ${50}^{\circ }\text{C}$ when the power supplied by the heater is $30\text{W}$ and the surrounding temperature is ${20}^{\circ }\text{C}$. As the heater is switched off, the liquid starts cooling and it was observed that it takes $10\text{sec}$ for temperature to fall from ${40}^{\circ }\text{C}$ to ${39.9}^{\circ }\text{C}$. Calculate the specific heat capacity of the liquid. Assume Newton's law of cooling to be applicable.

A monochromatic beam of light of wavelength $6000\stackrel{o}{\text{A}}$ in vacuum enters a medium of refractive index $1.25$. In the medium its wavelength and its frequency are

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two non-zero vectors, then the value of $(\overrightarrow{A}\times \overrightarrow{B})\times (\overrightarrow{A}-\overrightarrow{B})$ is

A particle of mass $1\text{kg}$ and charge $-{10}^{-2}\text{C}$ is constrained to move along the axis of a ring of radius $\sqrt{2}\text{m}$. The ring carries a uniform charge density $+40\text{nC/m}$ along its length. Initially, the particle is in the centre of the ring where the force on it is zero. The period of oscillation of the particle when it is displaced slightly from its equilibrium position is given by

Consider an equation represented by,

$b=\frac{ma}{k}\left[\sqrt{1+\frac{2kl}{ma}}\right]$, where, $m$ represents mass, $a$ represents acceleration, $l$ represents length and $k$ is a constant. The SI unit of $b$ should be

A
manometer reads the pressure of a gas in an enclosure as shown in
Fig. 10.25 (a) When a pump removes some of the gas, the manometer
reads as in Fig. 10.25 (b) The liquid used in the manometers is
mercury and the atmospheric pressure is 76 cm of mercury.

(a)
Give the absolute and gauge pressure of the gas in the enclosure for
cases (a) and (b), in units of cm of mercury.

(b)
How would the levels change in case (b) if 13.6 cm of water
(immiscible with mercury) are poured into the right limb of the
manometer? (Ignore the small change in the volume of the gas).

A steel tube of length 1.00 m is struck at one end. person with his ear close to the other end hears the sound of the blow twice, one travelling through the body of the tube and the other through the air in the tube. A Find the time gap between the two hearings. Use the table in the text for speeds of sound in various substances.

A pulse shown here is reflected from the rigid wall A and then from free end B. The shape of the string after these two reflections will be

A beam of electrons is moving with constant velocity in a region having electric and magnetic field of strength $20{\text{Vm}}^{-1}$ and $0.5\text{T}$ at right angles to the direction of motion of the electrons. What is the velocity of the electrons?

In the circuit as shown in figure, if all the symbols have their usual meanings, then identify the correct option.

Figure shows two blocks connected by a light string placed on the two inclined parts of a triangular structure. The coefficients of static and kinetic friction are $0.28$ and $0.25$ respectively at each of the surfaces. Find the minimum and maximum values of $m$ for which the system remains at rest. (Both in $\text{kg}$)

Three concentric spherical metallic shells A, B and C of radii $a,b$ and $c(a<b<c)$ have surface charge densities $\sigma ,-\sigma$ and $\sigma ,$ respectively.
If shells A and C are at the same potential, the relation between the radii $a,b$ and $c$ is