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Find the time period of the motion of the particle shown in figure (12-E14). Neglect the small effect of the bend near the bottom.

Angular velocity of a body moving on a circular track is given by $\overrightarrow{\omega }=\hat{i}+\hat{j}+\hat{k}$ and the radius vector $\overrightarrow{r}=2\hat{i}-2\hat{j}-2\hat{k}$ at the instant of time $‘t^{\prime }$. Then the magnitude of linear velocity of the body at that instant is.

A
parallel plate capacitor (Fig. 8.7) made of circular plates each of
radius R =
6.0 cm has a capacitance C =
100 pF. The capacitor is connected to a 230 V ac supply with a
(angular) frequency of 300 rad s⁻¹.

(a)
What is the rms value of the
conduction current?

(b) Is
the conduction current equal to the displacement current?

(c) Determine
the amplitude of B at
a point 3.0 cm from the axis between the plates.

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to ${\left(\frac{3}{4}\right)}^{\text{th}}$ of the original length (mass per unit length remains same) and the tension is changed. The factor by which the tension is to be increased is

A block is placed on a rough horizontal plane. A time dependent horizontal force F = Kt acts on the block. Here, K is positive constant. Acceleration - time graph of the block is

The output Y of the logic circuit shown in figure is best represented as:

If a charged particle goes undeflected in a region containing electric and magnetic fields. Select all of the following statements that must be true for this.

A modern Grand Prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is ${\mu }_s$, then the magnitude of negative lift $F_1$ acting downwards on the car is -



$($Assume forces on the four tyres are identical and $g=$ acceleration due to gravity$)$

Current $I_1$ and $I_2$ flow in the wires as shown in the figure. The field is zero at a distance $x$ to the right of O. Then,

A box contains n molecules of a gas. How will the pressure of the gas be effected, if the number of molecules is made 2n

In figure, the coefficient of static friction between the floor and block $B$ is $0.30$. The coefficient of static friction between the block $B$ and $A$ is $0.15$. The mass of block $A$ is $\frac{m}{2}\text{kg}$ and $B$ is $m\text{kg}$. What is the maximum horizontal force $F$ in $\text{Newtons}$ that can be applied to block $B$, so that the two blocks move together?

An object is to be seen through a simple microscope of focal length $10\text{cm}$. Where should the object be placed to produce maximum angular magnification? (The least distance for clear vision is $30\text{cm})$.

A hot air balloon is rising with an acceleration of 10 $m/s^2$. The moment when its velocity is 10 m/s, a stone is dropped which of the following is the displacement time graph of the stone with respect to the balloon.

A photon has energy of 2.6 eV. What is its wavelength?

A force $F=5+2x+3x^2$ acts on a particle in $x$ direction where $F$ is in Newton and $x$ is in meter . Find the workdone by this force during a displacement from $x=1\text{m}$ to $x=2\text{m}$.

For the given close packed structure of a salt made of cation $X$ and anion $Y$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately

$\text{packing fraction =}\frac{\text{packing efficiency}}{100}$

Let the radius and the height of a right circular cylinder is related as $r^2+h=6$. If the volume of the cylinder is maximum, then $\frac{r}{h}$ is -

A pitcher with 1 -mm thick porous walls contains 10 kg of water. Water comes to its outer surface and evaporates at the rate of $0.1g{s}^{-1}$. The surface are aof the pitcher (one side) = 200 $c{m}^2$. The room temperature = ${42}^{\circ }$, latent heat of vaporization = $2.27\times {10}^{6}Jk{g}^{-1}$, and the thermal conductivity of the porous walls = $0.80J{s}^{-1}{m}^{-1\circ }{C}^{-1}$. Calculate the temperature of water in the pitcher when it attains a constant value.

An interference is observed due to two coherent sources $A$ and $B$, having zero phase difference and separated by $4\lambda$, along the y-axis as shown in the figure (where $\lambda$ is the wavelength of the source). A detector $D$ is moved on the positive $x$-axis. The number of points on the $x$-axis, excluding the point $x=0$ and $x=\infty$, at which a maxima will be observed, are,

The factors on which the pressure exerted by a body depends

A vector that is perpendicular to both the vectors $\overrightarrow{a}=\hat{i}-2\hat{j}+\hat{k}$ and $\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k},$ is

The ratio of Boyle’s temperature and critical temperature for a gas is

In an ideal pulley particle system, mass $m_2(>m_1)$ is connected with a vertical spring of stiffness $k$. If mass $m_2$ is released from rest, when the spring is undeformed, find the maximum compression of the spring.

Q. resultant of which of the following may be equal to zero

a) 10N ,10N, 10N

b)10N,10N,25N

c)10N,10N,35N

The magnetic field at the centre of an equilateral triangular loop of side $2L$ and carrying a current $i$ is

An angular
magnification (magnifying power) of 30X is desired using an objective
of focal length 1.25 cm and an eyepiece of focal length 5 cm. How
will you set up the compound microscope?

A part of circuit is given here if $V_A-V_B=4V$ then find charge in 4mF capacitor

For a uniformly charged ring of radius $R$, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then the value of $h$ is:

When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60°with horizontal, it can travel a distance $x_1$ along the plane. But, when the inclination is decreased to 30° and the same object is shot with the same velocity, it can travel $x_2$ distance. Then $x_1:x_2$ will be

A ship is travelling due east at $10\text{km/hr}$. Another ship heading ${30}^{\circ }$ east of north is always due north from the first ship. The speed of the second ship in $\text{km/hr}$ is

Find the eelectric force btween two protons separated bya distance of 1 fermi $(1fermi=10-15)$ the protons in a nucleus remain at a separation of this order.