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Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy by 75% of the total energy?

A
system has two charges q_A
= 2.5 × 10⁻⁷
C and q_B
= −2.5 × 10⁻⁷
C located at points A: (0, 0, − 15 cm) and B: (0, 0, + 15 cm),
respectively. What are the total charge and electric dipole moment of
the system?

Air is blown through a pipe $AB$ at a rate of $15\text{L/min}$. The cross-sectional area of the broad portion of the pipe $AB$ is $2{\text{cm}}^2$ and that of the narrow portion is $0.5{\text{cm}}^2$. Find the approximate value of difference in water level $h$. (Density of air, ${\rho }_{\text{air}}=1.32{\text{kg/m}}^3$)

A stone of mass $2\text{kg}$ is projected from ground with speed $20\text{m/s}$ at angle ${30}^{\circ }$ with horizontal. The centripetal force acting on the object $1s$ after projection is

A uniform chain of length $l$ and mass $m$ lies on a smooth table. A very small part of this chain hangs from the table. It begins to fall under the weight of the hanging end. Find the velocity of the chain when the length of the hanging part becomes $y$.

A rectangular loop ABCD, carrying a current 15 A, is placed near a long wire carrying a current 40 A. The resultant force acting on the loop is

The potential energy of an electron in hydrogen atom is $-6.8\text{eV}$. Indicate in which excited state, the electron is present?

A disc having radius $r=1\text{m}$ and $m=2\text{kg}$ is rotating about an axis passing through its COM and perpendicular to the plane of disc. Initial velocity of a point $A$ at the edge of disc is $6\text{m/s}$. A retarding torque of magnitude $2\text{Nm}$ starts acting on disc about its axis of rotation. Find the velocity of point $A$ after $t=2\text{s}$.

A train $A$ runs from east to west and another train $B$ of the same mass and speed runs from west to east along the equator. $A$ presses the track with a force $F_1$ and $B$ with $F_2$. Then:

A soap film is made by dipping a circular frame of radius $b$ in soap solution. A bubble is formed by blowing air with speed $v$ in a cylindrical column. The radius of the bubble formed $R>>b$. If the air is incident normally on the surface of the bubble and air stops after striking the surface, then the radius $R$ of the bubble when the soap bubble separates from the ring is:

(Surface tension of liquid is $S$ and density of air is $\rho$)

A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with period

Two coils of self inductance $L_1$and $L_2$ are placed closer to each other so that total flux in one coil is completely linked with other. If is mutual inductance between them, then

From point $A$ located on a highway, one has to get as soon as possible, by a car, to point $B$ located in a field off the highway, at a distance $l$ from point $D$. If the car moves $n$ times slower in the field, at what distance $x$ from $D$ must one turn off the highway?

In the circuit given below, the value of the current is

Refractive index of the medium on the left and right side of the spherical surface are $1$ and $1.5$ respectively. For the arrangement of object and spherical refracting surface as shown in figure, the position of image will be

Light of frequency 3 times the threshold frequency is incident on photosensitive material. If the frequency is half and intensity is double . The photoelectric current becomes _____________

If the time of flight of a bullet over a horizontal range $R$ is $T$, then inclination of the direction of projection with the horizontal is

In an AC circuit, an alternating voltage, $V=200\sqrt{2}\sin \left(100t\right)$, is connected to a capacitor of capacitance $1\mu F.$ The rms value of the current in the circuit is -

A spherical ball of mass $4m$, density $\sigma$ and radius $r$ is attached to a pulley-mass system as shown in the figure. The ball is released in a beaker with a liquid of coefficient of viscosity $\eta$ and density $\rho (<\frac{\sigma }{2})$. If the length of the liquid column in the beaker is sufficiently long, the terminal velocity attained by the ball is given by: (Assume all pulleys to be massless and strings to be massless and inextensible):

A body is thrown with the velocity $u$ at an angle $\theta$ with the horizontal. If the body remains in air for 6 seconds, the maximum height reached by the body will be

What are the dimensions of Stefan’s constant?

A company manufactures two types of screws A and B. All the screws have to pass thorugh a threading machine and a slotting machine. A box of type A screws requires 2 min on the threading machine and 3 min on the slotting machine. A box of type B screws requires 8 min on the threading machine and 2 min on the slotting machine. In a week, each machine is available for 60 h. On selling these screws, the company gets a profit of Rs 100 per box on type A screws and Rs 170 per box on type B screws.

Formulate this problem as a LPP given that the objective is to maximise profit.

Refer to the circuit shown in figure, what inputs of $X$ and $Y$ will produce a high output at $R?$

A wire in a shape of parabola, $y=4x^2$ is located in a uniform magnetic field $B$ which is perpendicular to the $xy$ plane. At $t=0$, an infinitely long wire starts translation from the parabola vertex with constant acceleration $a$. The induced emf $e$ in the loop, thus formed as a function of $y$ is :

Suppose
that the electric field amplitude of an electromagnetic wave is E₀
= 120 N/C and that its frequency is ν
= 50.0 MHz. (a) Determine, B₀,
ω, k,
and λ. (b) Find expressions
for E and
B.

a cricket ball of mass 150 gram moving at 36 M per second strikes a back and returns back along the same lines at 21 m per second what is the change in momentum produced if that reminds in contact with the ball for 1 \ 20 seconds what is the average force exerted in Newton

In which of the following situations the heavier of the two particles has smaller de Broglie wavelength? The two particles