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A Particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x-$direction. It enters a region containing a uniform magnetic field $\overrightarrow{B}$ directed along the negative $z-$direction, extending from $x=a$ to $x=b$. The minimum value of $v$ required so that the particle can just enter the region $x>b$ is-

An open car is moving on a road with a speed if 100km/h.A man sitting in the car fires a bullet from the gun in the opposite direction.If the speed of the bullet is 250km/h relative to car,find its bullets speed with respect to ground? Will it be -150 km/h or 150km/h??

A block of weight $10N$ is fastened to one end of a wire of cross-sectional area $3m{m}^2$ and is rotated in a vertical circle of radius $20cm$. The speed of the block at the bottom of the circle is $2m{s}^{-1}$. If the Young modulus of the material of the wire is $2\times {10}^{11}N{m}^{-2}$, what is the elongation of the wire when the block is at the bottom of the circle?

X-rays are

Find the speed of uniform solid sphere after rolling down (without sliding) an inclined plane of vertical height $h=0.14\text{m}$ from rest is (Take $g=9.8{\text{m/s}}^2$)

Two blocks of masses $m_1$ and $m_2$ inter connected by a spring of stiffness $k$ are placed on a horizontal surface. If a constant horizontal force $F$ acts on the block $m_1$ it slides through a distance $x$ whereas $m_2$ remains stationary. If the coefficient of friction between all contacting surfaces is $\mu$, find the speed of the block $m_1$ as the function $x$.

An electric field of $1000\text{V/m}$, is applied to an electric dipole moment of ${10}^{-29}C\cdot m.$ What is the potential energy of the electric dipole?

Give the magnitude and direction of the net force acting on

(a) a drop of rain falling down with a constant speed,

(b) a cork of mass 10 g floating on water,

(c) a kite skillfully held stationary in the sky,

(d) a car moving with a constant velocity of 30 km/h on a rough road,

(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.

Find the accelerations $a_1,a_2,a_3$ of the three blocks shown in figure (6-E8) if a horizontal force of 10 N is applied on (a) 2 kg block, (b) 3 kg block (c) 7 kg Block. Take g = $10m/s^2$

A particle is moving along a circle of radius $1\text{m}$ with an angular speed $\omega =2t^2+5$, the tangential acceleration of the particle after $2\text{seconds}$ is

A pendulum clock that keeps correct time on the earth is taken to the moon. It will run

Using the formula $\overrightarrow{F}=\overrightarrow{qv}\times \overrightarrow{B}$ and $B=\frac{{\mu }_{0}i}{2\pi r}$ , show that the SI units of the magnetic field B and the permeability constant ${\mu }_0$ may be written as $Nm{A}^{-1}$ and $N{A}^{-2}$ respectively.

A point source of light is placed at a distance $2\text{m}$ below the surface of a large and deep lake. The fraction of light that escapes directly from water surface will be $({\mu }_{water}=4/3$)



$[$ Absorbtion of light within the water and reflection at surface except where it is total, have been neglected $]$

A rocket of mass $3000\text{kg}$ is launched with an exhaust speed of the gas $v=50\text{m/s}$. What will be the acceleration of the rocket after $3sec$, if the rate of consumption of fuel is $600\text{kg/s}$?

(Take $g=10{\text{m/s}}^2)$

Two electrons are moving toward each other each with a velocity of ${10}^6$ m/s what will be the closest distance of approach between them.

A body of mass $m$ falls from rest through a height $h$ under gravitation acceleration $g$ and is then brought to rest by penetrating through a depth $d$ into some sand. The average deceleration of the body during penetration into sand is

A cyclist starts from centre O of a circular park of radius 1km and moves along the path OPRQO as shown in figure. If the maintains constant speed of $10m{s}^{-1}$, what is his acceleration at point R?

In stationary waves all particles between two nodes pass through the mean

position

What is the horizontal deflection at free end C of the frame shown in the given figure ?

In the figure the string has a mass $4.5\text{g}$. How much time will it take for a transverse disturbance produced at the floor to reach the pulley ?

(Take $g=10{\text{ms}}^{-2}$ and assume that tension in the string is constant throughout)

The charge on the $4\mu \text{F}$ capacitor in the given circuit is ____ (in $\mu \text{C})$.

What is dielectric brake in topic atmospheric electricity

The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f =C$m^x{K}^y$; where C is a dimensionless quantity. The value of x and y are

The force exerted by a stretched chord at given displacements is shown in the table given below. Experimentally, the force is found to vary proportionally to the square of the displacement, i.e. $F\left(x\right)=-h{x}^2$ where $h$ is some constant.

If the potential energy at $x=0\text{m}$ is $U_0=0\text{J}$, determine the potential energy at $x=1.5\text{m}$.

A string is wrapped over a solid cylinder of mass $5kg$ and radius $1m$. When $40N$ force is applied tangentially on cylinder as shown, determine its angular acceleration about centre in $rad{s}^{-2}$(floor is smooth).

When a point source of light is at a distance of one meter from a photo cell, the cut off voltage is found to be $V$. If the same source is placed at $2\text{m}$ distance from photo cell, the cut off voltage will be -