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A particle of mass $m$ is projected with a speed of $u$ from the ground at an angle $\theta =\frac{\pi }{3}$ w.r.t. horizontal $\left(\text{x-axis}\right)$. When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\hat{i}$. The horizontal distance covered by the combined mass before reaching the ground is:

A
magnetic field set up using Helmholtz coils (described in Exercise
4.16) is uniform in a small region and has a magnitude of 0.75 T. In
the same region, a uniform electrostatic field is maintained in a
direction normal to the common axis of the coils. A narrow beam of
(single species) charged particles all accelerated through 15 kV
enters this region in a direction perpendicular to both the axis of
the coils and the electrostatic field. If the beam remains
undeflected when the electrostatic field is 9.0 ×
10⁻⁵
V m⁻¹,
make a simple guess as to what the beam contains. Why is the answer
not unique?

Question 19

If the materials used for constructing a building were good conductors, do you think lightning will strike the building? Will the lightning conductor be still required to be installed in the building?

If the intensity of a wave at a distance $r$ from a point source is $A,$ the intensity at distance $2r$ will be-

The electric potential V at a point P(x,y,z) in space is given by V=4x^{​​​​​​​​​​2} volt. Electric field at a point(1m,0,2m) in V/m is..

A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body?

Two particles A and B are moving as shown in the figure. At this moment of time, the angular speed of B with respect to A is

During compression of a spring the work done is $10\text{kJ}$ and $2\text{kJ}$ escaped to the surroundings as heat. The change in internal energy, $\Delta U$ (in $\text{kJ}$) is:

Q1. Liquid have generally have lower density as compared to solids. But you must have observed that ice floats on water. Find out why?

In the figure shown a particle $P$ strikes the inclined smooth plane horizontally and rebounds vertically. If the angle $\theta$ is ${60}^{\circ }$, then the coefficient of restitution is :

If the system shown in the figure is at rest, find the value of $m$

An elctric dipole of dipole moment $\overrightarrow{p}=(3\hat{i}+3\sqrt{3}\hat{j})C-m$ , is kept in $\overrightarrow{E}=40N/C\hat{i}$, what is the rate of change of angular momentum on it?

What is the equivalent resistance between $\text{A}$ and $\text{B}$ in the given network?

The figure shows three rotating, uniform discs that are coupled by belts. One belt runs around the rims of discs $A$ and $C$. Another belt runs around a central hub on the disc $A$ and the rim of the disc $B$. The belts move smoothly without slippage on the rims and hub. Disc $A$ has radius $R$; its hub has radius $0.500R$; disc $B$ has radius $0.250R$ and disc $C$ has radius $2.00R$. Discs $B$ and $C$ have the same density $($mass per unit volume$)$ and thickness. What is the ratio of the magnitude of the angular momentum of the disc $C$ to that of the disc $B$ ?

The maximum $\text{K.E.}$ of a oscillating spring is $5\text{J}$ and its amplitude $10\text{cm}$. The force constant of the spring is:

A silicon diode which has a knee voltage of 0.7 V & negligible forward resistance has a pd across it as shown. Then the current through the diode is

Three identical point masses, each of mass 1 kg lie in the x-y plane at points (0,0,0), (0,0.2m) and (0.2m, 0). The net gravitational force on the mass at the origin is

If $\overrightarrow{r}.\hat{i}=\overrightarrow{r}.\hat{j}=\overrightarrow{r}.\hat{k}\text{and}|\overrightarrow{r}|=3,\text{then}\overrightarrow{r}$ is equal to

Calculate $sin{15}^o.cos{15}^o$.

The plates of a parallel plate capacitor have an area of $90c{m}^2$ each and are separated by $2mm$. The capacitor is charged by connecting it to a $400V$ supply. Then the energy density of the energy stored $\left(inJ{m}^{-3}\right)$ in the capacitor is (Take ${ϵ}_0=8.8\times {10}^{-12}F{m}^{-1}$)

If pressure P, velocity V and time T are taken as fundamental physical quantities, the dimensional formula of force is

A circular coil of area 200 cm² and 25 turns rotates about its vertical diameter with an angular speed of 20 ms^-1 in a uniform horizontal magnetic field of magnitude 0.05 T. The maximum voltage induced in the coil is

Water surface profiles that are asymptotic at one end and terminated at the other end would include

If the arcs of the same length in two circles subtend angles ${45}^{\circ }$ and ${135}^{\circ }$ at the centre, find the ratio of their radii.

A cricket ball of mass m moving horizontally with a velocity v hits a wall and comes to rest instantaneously. What is the change in its entropy during the process, assuming that both the ball and the wall are perfectly rigid and there is no heat transfer during the process ?

Terminals of AC changes at a rate of 50 times per second so it should not have been possible to charge any device as it would get charged and discharged at every second but we fimd that this is not the case. May I know the reason why although the terminals change but the effect of current is not neutralised?

Steam at ${100}^{o}C$ is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at ${15}^{o}C$ till the temperature of the calorimeter and its contents rises to ${80}^{o}C$. The mass of the steam condensed in kg is

In a hydrogen atom, the electron and proton are bound at a distance
of about 0.53 Å:

(a) Estimate the potential energy of the system in eV, taking
the zero of the potential energy at infinite separation of the
electron from proton.

(b) What is the minimum work required to free the electron,
given that its kinetic energy in the orbit is half the magnitude of
potential energy obtained in (a)?

(c) What are the answers to (a) and (b) above if the zero of
potential energy is taken at 1.06 Å separation?