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Velocity of five particles $A,B,C,D$ and $E$ varies with time $t$ as, $\overrightarrow{V_A}=(8t\hat{i}+6\hat{j})m{s}^{-1},\overrightarrow{V_B}=(4\hat{i}+3\hat{j})m{s}^{-1},$
$\overrightarrow{V_C}=(6\hat{i}-4t\hat{j})m{s}^{-1},\overrightarrow{V_D}=(-3t\hat{i}+5\hat{j})m{s}^{-1}$ and $\overrightarrow{V_E}=(2\hat{i}+5t\hat{j})m{s}^{-1}.$
Match the pseudo force as observed and specified in column $I$ to the respective direction given in column $II$.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \left(A\right)\text{On A as observed by B}& \left(p\right)\text{Along positive X direction}\\ \left(B\right)\text{On B as observed by C}& \left(q\right)\text{Along negative X direction}\\ \left(C\right)\text{On C as observed by D}& \left(r\right)\text{Along positive Y direction}\\ \left(D\right)\text{on D as observed by E}& \left(s\right)\text{Along negative Y direction}\\ \left(E\right)\text{On E as observed by A}& \left(t\right)\text{zero}\end{array}$

Find minimum value of F such that $m_2$ starts its motion on the ground

In case of London forces ,if the distance between the particles is doubled how is the energy affected and by what factor is the energy is affected

A long metallic bar is carrying heat from one of its ends to the other end under steady state. The variation of temperature $\theta$ along the length $X$ of the bar from its hot end is best described by which of the following figures?

Question 1

What do you mean by free fall?

For the travelling harmonic wave

y (x, t) = 2.0 cos 2π (10t –
0.0080x + 0.35)

Where x and y are in cm and t in s. Calculate
the phase difference between oscillatory motion of two points
separated by a distance of

(a) 4 m,

(b) 0.5 m,

(c)
,

(d)

A block of a mass m kg moving with kinetic energy 3J on a smooth horizontal surface hits the free end of a spring, whose other end is attached to a rigid wall as shown in the figure. If restoring force applied by the spring is given by $f\left(x\right)=-2x-x^3(N{)}_b$ Then the maximum compression in the spring approximately

Two identical beads, each have a mass $m$ and charge $q$. When placed at a distance $R$ apart in a hemispherical bowl of radius $R$ with frictionless, non-conducting walls, the beads are at equilibrium as shown in figure. Determine the charge on each bead, if $m=0.001\text{kg}$ and $R=0.001\text{m}$

An earth satellite is moved from one stable circular orbit to a farther stable circular orbit. which one of following quantity increases

A double star is a system of two stars of masses $m$ and $2m$, rotating about their centre of mass only under their mutual gravitational attraction. If $r$ is the separation between these two stars, then their time period of rotation about their centre of mass will be proportional to?

A series $L-R$ circuit is connected to a battery of emf $E$ at $t=0$ as shown in the figure. The rate of increment of energy in the inductor with the time is best represented by-

Assuming frictionless contact everywhere, determine the magnitude of external horizontal force $P$ applied at the lower end for equilibrium of the rod as shown in figure. The rod is uniform and its mass is ${}^{\prime }{m}^{\prime }$.

A simple pendulum is oscillating in a vertical plane. If resultant acceleration of bob of mass $m$ at a point $A$ is in horizontal direction, find the tangential force at this point in terms of tension $\left(T\right)$ and weight of pendulum $\left(mg\right)$.

The area (in square units) of the region bounded by the curve $x=y^2\text{and}x=3-2y^2$ is

Two particles of masses $m_{1}and{m}_2$ in projectile motion have velocities ${\overrightarrow{v}}_{1}and{\overrightarrow{v}}_2$ respectively at time t = 0 and that is the moment when they collide. Their velocities become ${\overrightarrow{v}}_1^{\prime }and{\overrightarrow{v}}_2^{\prime }$ at time $2t_0$ while still moving in air. The value of magnitude of change in total momentum would be

A wave pulse moving to the right along the x-axis is represented by the wave function $y(x,t)=\frac{2.0}{(x-3.0t{)}^2+1}$ , where x and y are in centimeters and t is in seconds. (The maximum pulse height is defined as maximum displacement along y-axis). Then

A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, $A$ is the point of contact, $B$ is the centre of the sphere and $C$ is its topmost point. Then,

A body of mass $2\text{kg}$ is thrown vertically upwards with an initial speed of $10\text{m/s}$. The work done by the force of gravity during the time the body reaches its maximum height. (Consider $g=10{\text{m/s}}^2$)

A small source of sound S of frequency 500 Hz is attached to the end of a light string and is whirled in a vertical circle of radius 1.6 m. The string just remains tight when the source is at the highest point. (a) An observer is located in the same vertical plane at a large distance and at the same height as the centre of the circle (figure 16-E13). The speed of sound in air $=330m{s}^{-1}$ and $g=10m{s}^{-2}$. Find the maximum frequency heard by the observer. (b) An observer is situated at a large distance vertically above the centre of the circle. Find the frequencies heard by the observer corresponding to the sound emitted by the source when it is at the same height as the centre.

The magnetic susceptibility of a paramagnetic material at $-73{}^{\circ }\text{C}$ is $0.0075$. Its value at $-173{}^{\circ }\text{C}$ will be -



$[$Assume the states are far away from saturation$]$

For a transistor, the current amplification factor(α) is 0.8. The transistor is connected in common emitter configuration. The change in collector current, when the base current changes by 6 mA is

Which species has dipole moment?

The pressure exerted by $6\times {10}^{23}$ chlorine molecules, $n$ of which will strike per second on a wall of area $A$ at an angle ${60}^{\circ }$ with the normal, if the mass of $C{l}_2$ molecules is $m$ and speed of each $C{l}_2$ molecule is $v$, is given by :

A particle is fired upward with a speed of 20 km/s. The speed with which it will move in interstellar space is

A group of hydrogen atoms are prepared in n = 4 states. LKist the wavelength that are emitted as the atoms make transitions and return to n = 2 states.

A beam consisting of protons and electrons passed through perpendicular MF.The protons and electrons,

The potential energy of a particle executing S.H.M. is 2.5 J, when its displacement is half of amplitude. The total energy of the particle be

Initially the nucleus of radium – 226 is at rest. It decays due to which and a particle and the nucleus of radon are created. The released energy during the decay is 4.87 Mev, which appears as the kinetic energy of the two resulted particles. $[m_{\alpha }=4.002amu,m_{Rn}=222.017amu]$

What is the linear momentum of the a – particle?