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The position of a particle moving along x-axis is given by $x=(t^2-15t+10)\text{m}$, where $t$ is in second. Find the time when particle comes at rest?

Why only excess electrons flow during charging by conduction

Two cars $A$ and $B$ are travelling in the same direction with velocities $v_1$ and $v_2(v_1>v_2)$ respectively. When the car $B$ is at a distance $d$ ahead of the car $A$, the driver of the car $A$ applied the brake producing a uniform retardation $a$. There will be no collision if

Let $\left[{\epsilon }_0\right]$ denote the dimensional formula of the permittivity of vacuum. If $M=\text{mass},L=\text{length},T=\text{time and}A=\text{electric current}$, then :

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

Five identical conducting plates $1,2,3,4$ and $5$ are fixed parallel to and equidistant from each other as shown in figure. The equivalent capacitance between $\text{A}$ and $\text{B}$ is ($A=$ area of each plate)

Find the force of interaction between $3kg$ and $2kg$ bodies in the figure shown. (Take $g=10m/s^2$)

If ${\lambda }_v,{\lambda }_x$ and ${\lambda }_m$ represent the wavelengths of visible light, $X-$ rays and microwaves respectively, then -

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If $Q$ is doubled, the new resultant is perpendicular to $\overrightarrow{P}$. Then $R$ equals to

A simple pendulum is oscillating without damping. When the bob is at extreme position, acceleration vector is correctly shown by

A small particle of mass m is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius a. Motion occurs essentially in horizontal plane (assume gravity free space). The angular velocity of the cord is ${\omega }_0$ when the distance from the particle to the tangency point is $r_0$.

A coil of inductance 300mH and resistance 2Ω is connected to a source of voltage 2V. The current Reaches half of its steady state value in (approximately) $(lo{g}_{e}2=0.693)$

The logic circuit shown below has the input waveforms $\text{A}$ and $\text{B}$ as shown in the figure. Pick the correct output waveform

A small mass m is attached to a massless string whose other end is fixed at p as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at 0 and constant angular speed $\omega$. If the angular momentum of the system, calculated about o and p are denoted by $L_{o}and{L}_p$ respectively, then

An elevator in a building can carry a maximum of $10$ persons, with the average mass of each person being $68\text{kg}$. The mass of the elevator itself is $920\text{kg}$ and it moves with a constant speed of $3{\text{ms}}^{-1}$. The frictional force opposing the motion is $6000\text{N}$. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $(g=10{\text{ms}}^{-2})$ must be at least

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to :

The net capacitance of the system shown in the figure is -

An electric field $\left(2x\right)\text{V/m}\hat{i}$ and a magnetic field of constant value $2\text{T}\hat{i}$ exists in a region. If a charged particle of mass $1\text{kg}$ and having charge $1\text{C}$ is released from origin (0,0). what will be its speed when it has travelled $4\text{m}$ along $(+ve)x$ - axis?

Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be:

Two prisms $\text{A}$ and $\text{B}$ have dispersive powers of $0.012$ and $0.018$ respectively. The two prisms are in contact with each other. The prism $\text{A}$ produces a mean deviation of ${1.2}^{\circ }$, then the mean deviation produced by $\text{B}$ if the combination produces deviation without dispersion is

A capacitor of capacitance $C_1=1.0\mu F$ can with stand a maximum voltage $V_1=6.0kV$. Anothercapacitor of capacitance $C_2=2.0\mu F$ can withstand a maximum voltage $V_2=4.0kV.$ If the capacitors are connected in series, the combination can withstand a maximum voltage of

Two stones are thrown up simultaneously with initial speeds of $u_{1}and{u}_2(u_2>u_1).$ They hit the ground after 6 s and 10 s respectively. Which graph in figure correctly represents the time variation of $\Delta x=(x_2-x_1),$ the relative position of the second stone with respect to the first upto t = 10 s?

Assume that the stones do not rebound after hitting the ground.

A uniform square plate of side $a$ is hinged at one of its corners as shown. It is suspended such that it can rotate about horizontal axis. Find out its time period for small oscillations about its equilibrium position.

The component of vector $2\hat{i}-3\hat{j}+2\hat{k}$ perpendicualr to $\hat{i}+\hat{j}+\hat{k}$ is:

Obtain
the equivalent capacitance of the network in Fig. 2.35. For a 300 V
supply, determine the charge and voltage across each capacitor.

If a magnet is suspended at an angle ${30}^{\circ }$ to the magnetic meridian, it makes an angle of 45o with the horizontal. The real dip is

Four capacitors $C_1,C_2,C_3$ and $C_4$ of capacitance $3\mu \text{F},4\mu \text{F},6\mu \text{F}$ and $2\mu \text{F}$ are charged upto a potential difference of $2\text{V},3\text{V},4\text{V}$ and $4\text{V}$ respectively, if terminal $\text{a}$ is connected with $\text{f}$, terminal $\text{d}$ is connected with $\text{g}$, terminal $\text{e}$ is connected to $\text{h}$ and $\text{b}$ is connected $\text{c}$, then find the charge flows in the circuit?

If velocity of a particle is $v\left(t\right)=(15-3t)\text{m/s}$, the average speed of the particle in $6\text{sec}$ is

A particle of mass $m$ and charge $q$ is thrown from origin at $t=0$ with velocity $2\hat{i}+3\hat{j}+4\hat{k}\text{m/s}$ in a region with uniform magnetic field $\overrightarrow{B}=2\hat{i}\text{T}$. After time $t=\frac{\pi m}{qB}\text{sec}$, an electric field is switched on such that the particle moves on a straight line path with a constant speed. Then the electric field can be expressed as :

$(B$ is the magnitude of magnetic field $)$

A block of mass $15\text{kg}$ is resting on a rough inclined plane as shown in figure. The block is tied up by a horizontal string which has a tension of $50\text{N}$. The coefficient of friction between the surfaces of contacts is ($g=10{\text{m/s}}^2$)