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A particle moves in the x-y plane under the action of a force $\overrightarrow{F}=-2ksinkt(\hat{i}+\hat{j})$ at any time t its linear

momentum is given by P_X = 2cos (kt) and P_Y = 2cos (kt)The angle between $\overrightarrow{F}and\overrightarrow{P}$ at time t is

If the area of the region bounded by the curve $max(x,y)=1$ and $x^2+y^2=1$ in first quadrant is $a+\frac{\pi }{b}\text{sq.units}.$ Then which of the following statement(s) is/are correct ?

Determine the flux density inside a bar of aluminium that is positioned within a solenoid of wire $1.2\text{m}$ long and having $600$ turns, carrying a current of $8\text{A}$. Magnetic susceptibility of aluminium is $2.5\times {10}^{-4}$ .

A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer.

The resistance of a wire is $R\Omega$ . If it is melted and stretched to $n$ times its original length, its new resistance will be

1. 18.08

Different voltages are applied across a P-N junction and the currents are measured for each value. Which of the following graphs is obtained between voltage and current

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is

what will happen if we connect an ammeter in parallel. will it not measure the total current in the circuit?

In the given circuit the reading of ideal voltmeter is $E/2$. The internal resistance of the battery is

A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are $60\text{V}$ and $40\text{V}$ respectively.

At what frequency, the current in the circuit lags the voltage by ${45}^{\circ }$?

Force F is applied at an angle of 37° with horizontal on the block of mass m placed on the rough horizontal surface. If coefficient of friction is μ = 0.8, then value of F required to just move the block is



किसी खुरदरे क्षैतिज पृष्ठ पर रखे m द्रव्यमान के गुटके पर क्षैतिज के साथ 37° कोण पर बल F आरोपित किया जाता है। यदि घर्षण गुणांक μ = 0.8 है, तब गुटके को ठीक गति कराने के लिए आवश्यक F का मान है

The ejection of photoelectron from the silver metal in the photoelectric effect experiment can be stopped by applying the voltage of 0.35V when the radiation of 256.7 nm is used. Calculate the work fuction for silver metal.

A small mass $m$ starts sliding down a smooth and stationary semi-circular track. Which of the following graph best represents the variation of the magnitude of the force applied by the track on the mass and the angle $\theta$ ? ( assume initially $\theta =0$)

Two blocks $A$ and $B$ weighing $2\text{kg}$ and $8\text{kg}$ respectively are tied with an inextensible string. The coefficient of kinetic and static friction between the blocks and the horizontal surface is $0.25$ and $0.3$ respectively. If horizontal force $F=25\text{N}$, then find the acceleration of block $A$ and $B$.

The wires which connect
the battery of an automobile to its starting motor carry a current of
300 A (for a short time). What is the force per unit length between
the wires if they are 70 cm long and 1.5 cm apart? Is the force
attractive or repulsive?

A $50\text{kg}$ girl is swinging on a swing from rest. Then, the power delivered when moving with a velocity of $2\text{m/s}$ upwards in a direction making an angle ${60}^{\circ }$ with the vertical is

A solid cylinder and a hollow cylinder is having same mass $M$. Hollow cylinder is having the outer radius twice to that of solid cylinder. If $I_s$ and $I_h$ are the moment of inertia about the axis, along the height of the solid cylinder and hollow cylinder respectively passing through their centre, find the ratio of $I_h:I_s$.

A potential difference of 600 V is applied across the plates of a parallel plate capacitor. The separation between the plates is 3 mm. An electron projected vertically, parallel to the plates, with a velocity of $2\times {10}^{6}m{s}^{-1}$ moves undeflected between the plates. What is the magnitude of the magnetic field between the capacitor plates?

A planet P is moving in an elliptical path around the sun S. Speed of planet in positions P and Q are $v_1$ and $v_2$ respectively with SP= $r_1$ and SQ= $r_2$, then $\frac{v_1}{v_2}$ is equal to

In a hydrogen atom, the electron makes $6.6\times {10}^{15}\text{revolutions per second}$ around the nucleus in an orbit of radius $0.5\times {10}^{-10}\text{m}$. It is equivalent to a current nearly

The radii of circular orbits of two satellites $A$ and $B$ of the earth, are $4R$ and $R$, respectively. If the speed of satellite $A$ is $3V$, then the speed of satellite $B$ will be:

The lengths of spring are $l_1$ and $l_2$ when stretched with forces of $4N$ and $5N$ respectively. Its natural length is

The radii of two charged metal spheres are 5 cm and 10 cm both having same charge 75 mC. If they are connected by a wire, the quantity of charge transferred through the wire is

A large plane charge sheet having surface charge density $\sigma =2.0\times {10}^{-6}C{m}^{-2}$ lies in the x-y plane. Find the flux of the electric field through a circular area of radius $1cm$ lying completely in the region where x, y, z are all positive and with its normal making an angle of ${60}^{\circ }$ with the z-axis. (Given that the field due to infinite charged sheet is $\frac{\sigma }{2{ϵ}_0}$ where $\sigma$ = surface charge density. Also note that it is perpendicular to the sheet and is constant for all points from the sheet.)

A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?

In a guitar, two strings $A$ and $B$ made up of the same material produce beats of frequency $4\text{Hz}$. When the tension in $B$ is slightly decreased, the beat frequency increases to $6\text{Hz}$. If the frequency of $A$ is $530\text{Hz}$ then the original frequency of $B$ will be

If the wavelength of first member of Balmer series of hydrogen spectrum is $6564\dot{A}$, the wavelength of second member of Balmer series will be:

If u aan v are the objobj and image distances respectively due to convex lens then which among the following statements is false

(1)as u increases, v also increases

(2)as u increases, v decreases

(3) as u increases v remare constant

(4)None of the above

Two identical positive charges are placed on the y-axis at y = – a and y = + a. The variation of V (potential) along x-axis is shown by graph

A solid cylinder of mass $m$ is kept in balance on a fixed incline of angle $\alpha ={37}^{\circ }$ with the help of a thread fastened to its jacket. The cylinder does not slip. What will be the value of force $F$ that is required to keep the cylinder in balance when the thread is held vertically?

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$, a ray incident at an angle $\theta$, on the face AB would get transmitted through the face AC of the prism, provided