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The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to 6 s.

(Fig. 3.28)

What is the average speed of the particle over the intervals in (a) and (b)?

Vector $A$ having magnitude $\sqrt{2}$ units makes an angle ${45}^{\circ }$ with horizontal and vector $B$ having magnitude $2$ units makes an angle ${30}^{\circ }$ with horizontal as shown in the figure. What is $\overrightarrow{A}-\overrightarrow{B}$?

A light beam travelling in the $x-$ direction is described by the electric field $E_y=\left(300{\text{Vm}}^{-1}\right)\sin \omega (t-x/c)$. An electron is constrained to move along the $y-$direction with a speed of $2.0\times {10}^7{\text{ms}}^{-1}$. If the maximum electric force acting on the electron is $F_E$ and the maximum magnetic force acting on the electron is $F_B$, then

Find the angle between the net acceleration vector and tangential acceleration vector for a particle moving in a circle of radius $4\text{m}$. If its speed is increasing at $3\text{m/s}$ every second, at an instant when the speed of the particle is $4\text{m/s}$.

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4\mu F$ and $9\mu F$ capacitors), at a point distant $30m$ from it, would equal

A ray of light falls on a transparent sphere with centre at C as shown in figure. The ray emerges from the sphere parallel to line AB. The refractive index of the sphere is:

A student riding a bicycle on a $5km$ one way street takes $40min$ to reach home. The student stopped for $15min$. During the ride $60$ vehicles overtook the student (assume the no. of vehicles overtaken by the students is zero) during the ride and $45$ vehicles while the student stopped. The speed of vehicles stream on that road (in km/hr.) is.

The position $x$ of a moving particle at time $t$ is given by $x=t^2+2t+3\text{m}$. The average velocity of the particle during the first second of its motion is

A cord is wound a round the circumfererence of a wheel of mass 50Kg and diameter 0.3m. The axis of the wheel is horizonatal. A mass of 0.5Kg is attached at the end of the cord. Find the angular acceleration of the wheel?

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

A $100\text{W}$ bulb designed to operate on $100\text{V}$ is to be connected across a $500\text{V}$ source. Find the resistance to be put in series, so that bulb consumes $100\text{W}$ only.

A
bullet of mass 10 g and speed 500 m/s is fired into a door and gets
embedded exactly at the centre of the door. The door is 1.0 m wide
and weighs 12 kg. It is hinged at one end and rotates about a
vertical axis practically without friction. Find the angular speed of
the door just after the bullet embeds into it.

(Hint:
The moment of inertia of the door about the vertical axis at one end
is ML²/3.)

A stone projected vertically upwards from the ground reaches a maximum height h. When it is at a height $\frac{3h}{4}$, the ratio of its kinetic and potential energies is

Figure shows a cylindrical tube with adiabatic walls and fitted with an adiabatic separator. The separator can slide by an external mechanism. An ideal gas ($\gamma$ = 1.5) is injected in the two sides at equal pressure and temperature. The separator remains in equilibrium at the middle. It is now slid to a new position where it divides the tube in the ratio of 1 : 3. The ratio of temperature in part (1) to part (2) is

The pole- zero pattern of the active circuit shown below would be:

Seven identical circular planar discs, each of mass $M$ and radius $R$ are welded

symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $P$ is

A projectile is thrown with velocity 50m/s towards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53° with the horizontal and inclined plane is inclined at an angle of 45° to the horizontal. Find (a) time of flight (b) the distance between the point of projection and the foot of inclined plane.

In a p-n junction, the depletion region is 400 nm wide and an electric field of $5\times {10}^{5}V{m}^{-1}$ exists in it. (a) Find the height of the potential barrier. (b) What should be the minimum kinetic energy of a conduction electron which can diffuse from the n-side to the p-side ?

Which of the following nuclei shown in the graph is light and stable?

The current density at a point is $\overrightarrow{J}=(2\times {10}^4\hat{j}){\text{Am}}^{-2}$. Find the rate of charge flow through a cross-sectional area $\overrightarrow{S}=(2\hat{i}+3\hat{j}){\text{cm}}^2$.

The plane $2x-3y+6z-11=0$ makes an angle ${\sin }^{-1}\alpha$ with X-axis. The value of $\alpha$ is equal to

A stretched string is vibrating in the second overtone, then the number of nodes and antinodes between the ends of the string are respectively:

On a horizontal smooth plane, a particle collides with the rod hinged at one point(as shown in the figure) and sticks to it. Find the final angular velocity of the system.

$C_V$ and $C_P$ denote the molar specific heat capacities of a gas at constant volume and constant pressure,respectively. Then

Figure represents a capacitor made of two circular plates each of radius $r=12\text{cm}$ and separated by $d=5.0\text{mm}$. The capacitor is being charged by an external source. The charging current is constant current, $I=0.15\text{A}$.



Find the displacement current across the plates.

A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown. Initially the system is at rest when a particle of mass $m$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $v$, the speed with which the system moves just after collision is