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A straight wire carrying a current of 10 A is bent into a semi-circular arc of radius $\pi$ cm as shown in Fig. What is the magnitude and direction of the magnetic field at centre 0 of the arc?

A hemi-spherical bowl of radius $R=0.1\text{m}$ is rotating about its own axis (vertical) with uniform angular speed ${}^{\prime }{\omega }^{\prime }$. A particle of mass ${10}^{-2}\text{kg}$ on the smooth inner surface of the bowl is also rotating with the same $\omega$ at a height $h$ from the bottom of the bowl. What is the minimum value of ${}^{\prime }{\omega }^{\prime }$ to have a non-zero value of ${}^{\prime }{h}^{\prime }$, for which the particle remains at rest with respect to the bowl?

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

A wire of length $L$ , mass $m$ and carrying current $i$ is suspended from point ${}^{\prime }{O}^{\prime }$ as shown. An another infinitely long wire carrying the same current $i$ is at a distance $L$ below the lower end of the wire. Given $i=2\text{A},L=1\text{m}$ and $m=0.1\text{kg}$. $[\ln 2=0.693]$ At what distance $r$ from the suspended wire, the new wire (having the same current) should be palced to keep it stationary.

The wavelength of the radiation emitted by a body depends upon

An electromagnetic wave of v = 3MHz passes from vacuum into dielectric medium with $ϵ=4.0{ϵ}_0.$ Then:

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $\omega$, as shown int he figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $\left(\overrightarrow{\tau }\right)$ on the system about O, as a function of time is best represented by which plot?

For the LC circuit, whose graph of charge $\left(q\right)$ on capacitor versus time $\left(t\right)$ is shown in the figure. The frequency of oscillations of charge is -

According to the Collision theory, the rate of the reaction is:

Given in the figure are two blocks A and B of weight $20N$ and $100N$, respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between block B and the wall is $0.15$, the frictional force applied by the wall on block B is

A wooden ball of density $\sigma$ is released from the bottom of a tank which is filled with a liquid of density $\rho (\rho >\sigma )$ up to a height $h_1$. The ball rises in the liquid , emerges from its surface and attains a height $h_2$ in air. If viscous effects are neglected, the ratio $\frac{h_2}{h_1}$ is

The acceleration versus time graph for a particle moving along a straight line is shown in the figure. If the particle starts from rest at $t=0$, then its speed at $t=30\text{s}$ will be

In the given potentiometer circuit arrangement, the balancing length $\text{AC}$ is measured to be $250\text{cm}$. When the galvanometer connection is shifted from point $\left(1\right)$ to point $\left(2\right)$ in the given diagram, the balancing length becomes $400\text{cm}$. The ratio of the emf of two cells, $\frac{E_1}{E_2}$ is:

Test if the following equations are dimensionally correct :

(a) $h=\frac{2Scos\theta }{\rho rg}$,

(b) $u=\sqrt{\frac{P}{rho}}$,

(c) $V=\frac{\pi P{r}^{4}t}{8\eta l}$,

(d) $v=\frac{1}{2\pi \sqrt{\frac{mgl}{I}}}$;

where h = height, S = surface tension, $\rho$ = density, P = pressure, V = volume, $\eta$ = coefficient of viscosity, v = frequency and I = moment of inertia.

in your worksheet send for me in mail. in that page number 22 H.O.T.S 4th,5th question how to solve

1. 1.58

A
cyclist starts from the centre Oof a
circular park of radius 1 km, reaches the edge Pof the
park, then cycles along the circumference, and returns to the centre
along QO as
shown in Fig. 4.21. If the round trip takes 10 min, what is the (a)
net displacement, (b) average velocity, and (c) average speed of the
cyclist?

The total current supplied to the circuit by the battery is

When a point source of light is at a distance of one metre from a photo cell, the cut off voltage is found to be V. If the same source is placed at 2 m distance from photo cell, the cut off voltage will be

Three sources of sound $S_1,S_2$ and $S_3$ of equal intensity 'I' are placed in a straight line with $S_1{S}_2=S_2{S}_3$. At a point P, far away from the sources, the wave coming from $S_2$ is ${120}^{\circ }$ ahead in phase of that from $S_1$. Also, the wave coming from $S_3$ is 120° ahead of that from $S_2$. What would be the resultant intensity of sound at P?

What is electrical resistance ?

Two satellites A and B go round a planet P in circular orbits having radil 4R and R respectively. If the speed of the satellite A is 3V, the speed of the satellite B will be

A wire $\text{PQ}$ is placed near an infinitely long straight current carrying wire. If both the wires carry the same current and the long wire is kept fixed, which of the following correctly represents the graph of force $F$ vs $x$ ?

If a car travelling at $40\text{m/s}$ is to be brought to rest in a distance of $100\text{m}$, then its retardation should be

A spherical drop of water has $1\text{mm}$ radius. If the surface tension of water is $75\times {10}^{-3}\text{N/m}$, then the difference in pressure between the inside and outside of the drop is

Two small beads P and Q of equal mass ( = m) are connected by a light inextensible string. They are constrained

to move on a frictionless ring in a vertical plane. The blocks are released from rest as

shown in the figure. The tension in the string just after release is

The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity $v_0$ The distance travelled by the particle in time $t$ will be

Two cells of emf $E_1$ and $E_2$ are joined in opposition (such that $E_1>E_2$). If r1 and r2 be the internal resistance and R be the external resistance, then the terminal potential difference is

If force $F$ is applied for stretching a wire of length $L$ by $\Delta L$, then elastic potential energy stored per unit volume is
($A$ is cross sectional area of wire)

Input waveforms A and B as shown in figure are applied to the combination of gates as shown in fig. Which of the waveforms shown in (a,b,c,d) correctly represents the output waveform?

Four wires of equal lengths are bent in the shapes of four loops $\text{P},\text{Q},\text{R}$ and $\text{S}$ as shown in the figure. If each loop carries same current $I$ in the same sense, which loop will have highest magnetic moment ?

A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is $\theta$. Which of the following statements about its motion is/are correct?

Starting from $x_0=1$, one step of Newton-Raphson method in solving the equation $x^3+3x-7=0$ gives the next value $\left(x_1\right)$ as