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The breaking stress of a material is 108N/m, density of material is 3000kg/m3
. Find the greatest
length of wire that could hang vertically without breaking. (Pause the video and solve without
looking at the solution).

A steel wire is stretched by a certain amount under a load. if the load and the radius both are increasing to 4 times find the stretch cause in wire

The frequency of a wave of light is $12\times {10}^{14}{s}^{-1}$ . The wave number associated with the light is

The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child.
What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

Two drops of equal radii coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?

An object moves along the grid through the points A,B,C,D,E and F as shown in the figure. Find the distance covered by the moving object?

A stick is thrown in the air and lands on the ground at same distance from the thrower. The centre of mass of the stick will move along a parabolic path

In a game house the above punch bag has the shown set up. If you punch the bag at mean position and it gets compressed by a distance x m, then it will come back to mean and get elongated by the same distance x m. Rohit punches the bag and compresses it by 5 cm. What is the magnitude of maximum displacement (M) and magnitude of minimum displacement (m)?

What is the value of $\sin \left(\frac{31\pi }{3}\right)$?

Two resistors of resistance R1 =100±3 and R2 =200±4 .find the equivalent reaisresis in parallel combination

An uncharged parallel-plate capacitor having a dielectric of dielectric constant $K$ is connected to a similar air cored parallel-plate capacitor charged to a potential $V_0$. The two share the charge and the common potential becomes $V$. The dielectric constant $K$ is

A boy on a cycle pedals around a circle of 20 metres radius at a speed of The combined mass of the boy and the cycle is 90 kg. The angle that the cycle makes with the vertical so that it may not fall is $(g=9.8m/se{c}^2)$

When the tension in a metal wire is $T_1$, its length is $l_1$. When the tension is $T_2$, its length is $l_2$. The natural length of wire is

From the given graph (in red colour) match the mentioned points (column I)
with their slope (column II)
Column I Column II
(p) X = 2 (i) 2
(q) X = 6 (ii) 6
(r) X = 10 (iii) 10
(iv) 0
(v) $\frac{1}{2}$
(vi) $\frac{-1}{2}$

A block of mass m is placed on a wedge. The wedge can be accelerated in four manners marked as (1), (2), (3) and (4) as shown. If the normal reactions in situation (1), (2), (3) and (4) are $N_1,N_2,N_{3}and{N}_4$ respectively and acceleration with which the block slides on the wedge in situations are $b_1,b_2,b_{3}and{b}_4$ respectively then:

A tuning fork of frequency 440 Hz is attached to a long string of linear mass density $0.01kg{m}^{-1}$ kept under a tension of 49 N. The fork produces transverse waves of amplitude 0.50 mm on the string. (a) Find the wave speed and the wavelength of the waves. (b) Find the maximum speed and acceleration of a particle of the string. (c) At what average rate is the tuning fork tranmitting energy to the string ?

In a double slits interference experiment, the separation between the slits is 1.0 mm, the wavelength of light used is $5.0\times {10}^{-7}$ m and the distance of the screen from the slits is 1.0 m (a0 Find the distance of the centre of the first minimum from the centre of the central maximum. (b) how many bright fringes ar formed in one ventimetr width on the screen?

The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m,333 m/s, and 110 Hz. Write the equation of the wave.

A small ball of mass m suspended from the ceiling at a point O by a thread of length moves along a horizontal circle with a constant angular velocity ω. Which of the followings is /are correct?

Figure 3.24 gives the x-t plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest, and in which is it the least? Give the sign of average velocity for each interval.

A ball falls vertically onto a floor, with momentum $p$, then bounces repeatedly. The coefficient of restitution is $\frac{1}{2}$, the total momentum imparted on the ball by the floor (due to multiple collisions) is

A wire $ABC$ carrying current of magnitude $5A$ is placed in a region having horizontal magnetic field $0.15T$ as shown. If the wire $ABC$ resembles a right angled triangle at $A$,length of section $AB$ and $BC$ are $16cm$ and $20cm$ respectively.Then force on the section $BC$ due to magnetic field is____( Assume that current is flowing from $B$ to $C$)

A particle is sliding down a frictionless hemispherical bowl. It passes the point A at t=0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t =0 along the horizontal string AB (see figure) with the speed v. Friction between the bead and the string may be neglected. Let $t_P$ and $t_Q$ be the respective time taken by P and Q to reach the point B. Then

A projectile has a range R and time of flight T. If the range is doubled by increasing the speed of projection, without changing the angle of projection, the time of flight will become

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 ${ϵ}_0=8.8\times {10}^{-12}F{m}^{-1}$)

There are two mass less spring A and B of spring constant $K_A$ and $K_B$respectively and $K_A$ > $K_B$ If $W_A$ and $W_B$ be denoted as work done on A and work done on B respectively, then

Two bodies of masses $m_1$ and $m_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momentum, then ratio $p_1:p_2$ is equal to

Find the amplitude and phase of the vibrations given by $x=A\cos \omega t+\frac{A}{2}\cos (\omega t+\frac{\pi }{2})+\frac{A}{4}\cos (\omega t+\pi )+\frac{A}{8}\cos (\omega t+\frac{3\pi }{2})$

Three processes form a thermodynamic cycle as shown on P - V diagram for an ideal gas.
Process $1\to 2$ takes place at constant temperature $300\text{K}$.
Process $2\to 3$ takes place at constant volume.
During this process $40\text{J}$ of heat leaves the system.
Process $3\to 1$ is adiabatic and temperature $T_3$ is $275\text{K}$.
Work done by the gas during the process $3\to 1$ is

A free neutron beta-decays to a proton with a half-life of 14 minutes. (a) What is the decay constant ? (b) Find the energy liberated in the process.

A solid wood door has dimensions; height = 2m, width = 0.8m, thickness = 0.04m. Its thermal conductivity is $K=0.04J{s}^{-1}{m}^1{(}^{\circ }C{)}^{-1}$. The inside air temperature is ${20}^{\circ }C$ and outside air temperature is $-{10}^{\circ }C$. What is the rate of heat flow through the door, assuming the surface temperatures are those of the surrounding air.

Initially the circuit is in steady state. When the switch S is closed, the heat generated in the circuit will be :

A particle undergoes SHM according to $X=Asin(wt+\pi /3$). What would be the shortest time taken by it to move from $X=A/2$ to $X=-A/2$ ?

What is the respective number of $\alpha$ and $\beta$ particles emitted in the following radioactive decay?
${}^{200}{X}_{90}{\to }^{168}{Y}_{80}$

Consider two hollow glass spheres, one containing water and other containing mercury each liquid fills about one tenth of the volume of sphere in zero gravity environment

The mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum on this planet will be (If it is a second's pendulum on earth)

A particle starts from rest at time $t=0$ and moves on a straight line with acceleration as plotted in figure. The speed of the a particle will be maximum at time

Calculate the number of molecules present in 350 cm³ of NH3 gas at 273K and 2 atmospheric pressure.

Two long parallel wires P and Q are both perpendicular to the plane of the paper with distance 5 m between them. If P and Q carry current of 2.5 amp and 5 amp respectively in the same direction, then the magnetic field at a point half way between the wires is

A boy is standing inside a train moving with a constant velocity of magnitude $10m/s$. He throws a ball vertically up with a speed of $5m/s$ relative to the train. Find the radius of curvature of the path of the ball just at the time of projection. (Take $g=10m/s^2$)

Which of the following are not electromagnetic waves?

In which quadrant does the point $(-3,4)$ lie?

Find the slope of the tangent to the curve $y=4x^2-3x-8$ at point $(-3,4)$.

The x-z plane separates two media A and B with refractive indices $n_{1}and{n}_2$ respectively. A ray of light travels from A to B. Its directions in the two media are given by the unit vectors, $\overline{r_A}=a\hat{i}+b\hat{j}\&\overline{r_B}=\alpha \hat{i}+\beta \hat{j}$ respectively where $\hat{i}and\hat{j}$ are unit vectors in the x and y directions. Then

In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges are placed at (n – 1) corners. At the centre, the intensity is E and the potential is V. The ratio $\frac{V}{E}$ has magnitude.