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Variation of force $F$ acting on a body with time $t$ is as shown in figure. Change in momentum of the body in the interval $4\text{s}$ to $8\text{s}$ is

An ideal monatomic gas is confined in a cylinder by a spring-loaded piston of cross-section $8\times {10}^{-3}{m}^2$. Initially the gas is at $300K$ and occupies a volume of $2.4\times {10}^{-3}{m}^3$ and the spring is in a relaxed state. The gas is heated by a small heater coil $H$. The force constant of the spring is $8000N/m$ and the atmospheric pressure is $1.0\times {10}^{5}Pa$. The cylinder and the piston are thermally insulated. The piston is massless and there is no friction between the piston and the cylinder. Neglect heat loss through lead wires of the heater. The heat capacity of the heater coil is negligible. With all the above assumptions, if the gas is heated by the heater until the piston moves out slowly by $0.1m$, then the final temperature is

A wheel of mass $m=1\text{kg}$ and radius $r=1\text{m}$ is under pure rolling in a straight line as shown in figure.







If $V=2\text{m/s},a=1{\text{m/s}}^2,\alpha =1{\text{rad/s}}^2$ and $\omega =2\text{rad/s}$, find the torque and $K.E$ of the wheel about the contact point.

Electric field in a certain region is acting radially outward and the variation of electric field with distance from the origin is represented below. The slope of the graph is $A^{\prime }$.





The charge contained in a sphere of radius $a$ centred at the origin will be given by

A pipe 20 cm long is closed at one end. Which harmonic mode of the
pipe is resonantly excited by a 430 Hz source? Will the same source
be in resonance with the pipe if both ends are open? (Speed of sound
in air is 340 m s^–1).

Intensity is:

Three vectors $\overrightarrow{P},\overrightarrow{Q}$ and $\overrightarrow{R}$ are such that $|\overrightarrow{P}|=|\overrightarrow{Q}|,|\overrightarrow{R}|=\sqrt{2}|\overrightarrow{P}|$, and $\overrightarrow{P}+\overrightarrow{Q}+\overrightarrow{R}=\overrightarrow{0}$. The angles between $\overrightarrow{P}$ and $\overrightarrow{Q},\overrightarrow{Q}$ and $\overrightarrow{R}$, and $\overrightarrow{P}$ and $\overrightarrow{R}$ are

How to get electrostatic potential due to an electric dipole at any point

The intensity of magnetic field at point X on the axis of a small magnet is equal to the field intensity
at another point y on its equatorial axis. The ratio of X and Y from the centre of the magnet will be

A thick current carrying cable of radius $R$ carries current $I$ uniformly distributed across its cross-section. The variation of magnetic field $B\left(r\right)$ due to the cable with the distance $r$ from the axis of the cable is represented by

For the wave shown in figure, write the equation of this wave if its position is shown at t = 0. Speed of wave is v = 30 m/s.

A particle is projected at an angle ${60}^{\circ }$ with the horizontal with a speed $10m/s$.

Find angular velocity when particle reaches X-axis, about an axis passing through origin ang along Z-axis.

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

Experimental investigations show that the intensity of the solar radiation is maximum for a wavelength $4750\hat{A}$ in the visible region. If the surface temperature of the sun is 6000 K, what is the value of the Wien’s constant b?

The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of ${45}^{\circ }$ with the vertical, the escape velocity will be

The volume charge density as a function of distance $x$ from one face inside a unit cube is varying as shown in the figure. Then the total flux (in S.I. units) through the cube if $({\rho }_o=8.85\times {10}^{–12}\frac{C}{m^3})$ is :

A vessel contains oil (density = $0.8{\text{g/cm}}^3)$ over mercury (density = $13.6{\text{g/cm}}^3)$. A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in ${\text{g/cm}}^3$ is

Two blocks of masses $m_1$ and $m_2$ are connected by a spring of constant k (given figure).The block of mass $m_2$ is given a sharp impulse so that it acquires a velocity $v_0$ towards right.Find (a) the velocity of the centre of mass,(b) the maximum elongation that the spring will suffer.

A ball $A$ is falling vertically downwards with velocity $v_1$. It strikes elastically with a wedge moving horizontally with velocity $v_2$ as shown in figure. What must be the ratio so that the ball bounces back in vertically upwards direction relative to wedge?

The product of inertia of the area shown in figure about x and y axis is

In a simple pendulum experiment for determination of acceleration due to gravity $\left(g\right)$, time taken for $20$ oscillations is measured by using a watch of $1$ second least count. The mean value of time taken comes out to be $30\text{sec}$. The length of pendulum is measured by using a meter scale of least count $1\text{mm}$ and the value obtained is $55.0\text{cm}$. The percentage error in the determination of $g$ is close to,

A stretched string is vibrating according to the equation $y=5\sin \left(\frac{\pi x}{2}\right)\cos 4\pi t$, where $y$ and $x$ are in $\text{cm}$ and $t$ is in $\text{sec}$. The distance between two consecutive nodes on the string is

Suppose two deuterons must get as close as ${10}^{-14}$ in order for the nuclear force to overcome the repulsive electrostatic force. The height of the electrostatic barrier is nearest to

Three charges $Q,+q\text{and}+q$ are placed at the vertices of a right-angle isosceles triangle, as shown below. The net electrostatic energy of the configuration is zero, if the value of $Q$ is:

A particle of mass $5\text{kg}$ is dropped from a tower of height $10\text{m}$. Find the difference of work done by gravity from point $A$ to $B$ $\left(W_{AB}\right)$ and change in potential energy from $A$ to $B$ $\left(U_{AB}\right)$.

A stone is thrown at an angle $\theta$ to the horizontal reaches a maximum height H. Then the time of flight of stone will be