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A particle has the position vector $\overrightarrow{r}=\hat{i}-2\hat{j}+\hat{k}$ and the linear momentum $\overrightarrow{p}=2\hat{i}-\hat{j}+\hat{k}$. Then, its angular momentum about the origin is

What is general intuition of voltage

Magnetic field at any point due to bar magnet.

A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature and enclosed in the same surroungings. Then

A particle of mass $m$ moving in the $x-$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y-$ direction with speed $v$. If the collision is perfectly inelastic, then loss in energy$\left(\%\right)$ during the collision is close to

Water is moving with a speed of $5.18m{s}^{-1}$ through a pipe with a cross-sectional area of $4.20c{m}^2$. The water gradually descends 9.66 m as the pipe increase in area to $7.60c{m}^2$. The speed of flow at the lower level is

A parallel plate capacitor with air as medium between the plates has a capacitance of 10μF. The area of capacitor is divided into two equal halves

and filled with two media as shown in the figure having dielectric constant k₁=2 and k₂=₄. The capacitance of the system will now be

The magnetic intensity H at the centre of a long solenoid carrying a current of 2.0 A, is found to be 1500 A $m^{-1}$. Find the number of turns per centimetre of the solenoid.

An iceberg is floating in sea water. The density of ice is $0.92gm/c{m}^3$ and that of sea water is $1.03gm/c{m}^3$. What percentage of the iceberg will be below the surface of water

'tesla' is same as :

The de-Broglie wavelength of a particle accelerated with a p.d of 150 V is ${10}^{-10}m$. If it is accelerated with a p.d of 600 V, its wavelength will be

A screw gauge with a pitch of $0.5mm$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5mm$ and the 25th division coincides with the main scale line ?

A large parallel plate capacitor is made of two metal plates of size $2m\times 1m$. It has a dielectric slab made of two dielectrics of permeability $K_1$ and $K_2$ as shown in the figure, the distance between them being 0.1m. It is charged by a battery of 1000V after which the battery is disconnected. Now the dielectric slab is puled out by 10cm. The work done in doing so is (ignore the gap between the plates and the dielectric slab)

A mild-steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars, A mass m is suspended from the midpoint of the wire. Strain in the wire is

If a vector $\overrightarrow{P}$ making angles $\alpha ,\beta$ and $\gamma$ respectively with the X, Y and Z axes respectively.Then $si{n}^2\alpha +si{n}^2\beta +si{n}^2\gamma =$

In the arrangement shown in figure $m_A=m_B=2kg$. String is massless and pulley is frictionless. Block B is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is $\mu =0.5$. What maximum horizontal force F can be applied so that block A does not slip over the block B? $(g=10m/s^2)$

The percentage errors in a, b, c are $\pm 1\%,\pm 3\%$ and $\pm 2\%$ respectively. The percentage error in $x=\frac{a{b}^2}{c^3}$ can be

A mild-steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between
two pillars, A mass m is suspended from the midpoint of the wire. Strain in the wire is

A flexible wire loop in the shape of a circle has a radius that grows linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the radius of the loop, $B\left(r\right)\propto \frac{1}{r}$. How does the e.m.f, $ϵ$ vary with time?

A uniform rod of length $5\text{m}$ is placed along $x$ - axis as shown in the figure. The position of centre of mass of the rod from the origin is

Block A of mass $35\text{kg}$ is resting on a frictionless floor. Another block B of mass $7\text{kg}$ is resting on it as shown in the figure. The coefficient of static friction between the blocks is $0.5$ while kinetic friction is $0.4$. If a force of $100\text{N}$ is applied to block B, the acceleration of the block A will be $(g=10{\text{ms}}^{-2}):$

Find the period of small oscillations of the bob of mass $m$ shown in the figure. Given, mass of the rod is also $m$.

An object of mass $m$ is moving with velocity $\overrightarrow{u}$ towards a plane mirror kept on a stand as shown in the figure. The mass of the mirror and stand system is $m$. A head-on elastic collision takes place between the object and the mirror stand, the velocity of image before and after the collision is

Mass m shown in the figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light & smooth and strings light.

Two blocks of masses $2\text{kg}$ and $4\text{kg}$ are arranged as shown in figure. Then, find the maximum value of force $F$, for which both blocks will move together.

The graph between the displacement $x$ and time $t$ for a particle moving in a straight line is shown in figure. During the interval $OA,AB,BC$ and $CD$, the acceleration of the particle is

When a centimeter thick surface is illuminated with light of wavelength $\lambda$, the stopping potential is V. When the same surface is illuminated by light of wavelength $2\lambda$, the stopping potential is $\frac{V}{3}$. The threshold wavelength for the surface is

Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting the higher and the lower initial tension in the strings as T₁,T₂ respectively, then it could be said that while making the above changes in tension :

A total charge Q is broken in two parts $Q_1$ and $Q_2$ and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, when

The displacement of a particle executing SHM is given y = 0.25 sin 200t cm. The maximum speed of the particle is

From the following Receipts and Payments Account of Sonic Club and from the given additional information, prepare the expenditure on account of salaries for the year ending 31st March, 2015 and show the salaries item in the Income and Expenditure Account and the Balance Sheet as at 31st March, 2014 and 31st March, 2015.

An Extract of Receipts and Payments Account for the year ending 31st March, 2015
Dr. Cr.
$\begin{array}{cccc}\text{Expenditure}& \text{Rs}& \text{Income}& \text{Rs}\\ & & \text{By Salaries :}& \\ & & \text{2013-14}& 20,000\\ & & \text{2014-15}& 2,80,000\\ & & \text{2015-16}& 18,000\end{array}$

Additional Information Rs

(i) Salaries outstanding on 31st March, 2014 25,000

(ii) Salaries outstanding on 31st March, 2015 45,000

(iii) Salaries paid in advance on 31st March, 2014
10,000

three uniform spheres each having a mass M and radius a are kept in such a way that eac touches the other two. Find th magnitude of the gravitational force on any of the spheres due to the other two.

Two square blocks of size $a\times a$ is removed from a big square $4a\times 4a$ as shown in the figure. Find the COM of the system after removing the square blocks.

When we apply reverse bias to a junction diode it :

if $\overline{a},\overline{b},\overline{c}areunitvectorssuchthat\overline{a}.\overline{b}=\overline{a}.\overline{c}=0and(\overline{b},\overline{c})=\frac{\pi }{3}thenthevalueof|\overline{a}\times \overline{b}-\overline{a}\times \overline{c}|$ is

Steam at ${120}^{\circ }C$ is continuously passed through a 50 -cm long rubber tube of inner and outer radii 1.0 cm and 1.2 cm. The room temperature is ${30}^{\circ }C$. Calculate the rate of heat flow through the walls of the tube. Thermal conductivity of rubber = $0.15J{s}^{-1}{m}^{-1\circ }{C}^{-1}$.

A cyclotron designed to speed up protons which has a magnetic field of 0.8 Tesla over a region of radius 1.6 m, then maximum speed of protons $(q=1.6\times {10}^{-19}C,m=1.6\times {10}^{-27}kg)$

From a uniform square plate, one fourth part is removed as shown in figure. The centre of mass of remaining part will lie on line joining

Two spherical rain drops with radii in the ratio $1:2$ fall from a great height through the atmosphere. The ratio of their momenta after they have attained terminal velocity is:

There is a destructive interference between the two waves of wavelength $\lambda$ coming from two different paths at a point. To get maximum sound or constructive interference at that point, the path of one wave is to be increased by

If points A and B have a potential 3V and 5V respectively, and a dipole is brought between the two points, which way will its dipole moment align?
Given: Dipole is an arrangement of two equal and opposite charges separated by a very small fixed distance and Dipole moment is a vector quantity which points from negative to the positive charge of the dipole arrangement.

A gas is kept in a container at a constant temperature. Initial pressure of the gas is 1 atm. If the volume of container is reduced to $\frac{1}{4}$ of its initial volume, then new pressure will be