NTA JEE Main 9th January 2019 Shift 2 - Physics

The position co-ordinates of a particle moving in a 3D coordinate system is given by
$$x = a\cos\omega t$$
$$y = a\sin\omega t$$
and $$z = a\omega t$$
The speed of the particle is:

Expression for time in terms of $$G$$ (universal gravitational constant), $$h$$ (Planck constant) and $$c$$ (speed of light) is proportional to:

In a car race on straight road, car A takes a time $$t$$ less than car $$B$$ at the finish and passes finishing point with a speed $$v$$ more than that of car $$B$$. Both the cars start from rest and travel with constant acceleration $$a_1$$ and $$a_2$$ respectively. Then $$v$$ is equal to:

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45$$^{\circ}$$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ($$g = 10$$ m s$$^{-2}$$)

A force acts on a 2 kg object so that its position is given as a function of time as $$x = 3t^2 + 5$$. What is the work done by this force in first 5 seconds?

A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30$$^{\circ}$$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s$$^{-1}$$) will be: ($$g = 10$$ ms$$^{-2}$$)

The energy required to take a satellite to a height $$h$$ above the Earth surface (radius of Earth $$= 6.4 \times 10^3$$ km) is $$E_1$$, and the kinetic energy required for the satellite to be in a circular orbit at this height is $$E_2$$. The value of $$h$$ for which $$E_1$$ and $$E_2$$ are equal, is:

The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m$$^3$$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

Two carnot engines $$A$$ and $$B$$ are operated in series. The first one, $$A$$, receives heat at $$T_1 (= 600K)$$ and rejects to a reservoir at temperature $$T_2$$. The second engine $$B$$ receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $$T_3 (= 400K)$$. Calculate the temperature $$T_2$$ if the work outputs of the two engines are equal:

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature, 27$$^{\circ}$$C. The amount of heat transferred to the gas, so that R.M.S. velocity of molecules is doubled, is about. [$$R = 8.3$$ J (K mole)$$^{-1}$$]

A particle is executing simple harmonic motion (SHM) of amplitude $$A$$, along the $$x$$-axis, about $$x = 0$$. When its potential Energy (PE) equal kinetic energy (KE), the position of the particle will be:

A rod of mass $$M$$ and length $$2L$$ is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass $$m$$, are attached at a distance $$L/2$$ from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio $$m/M$$ is close to:

A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km h$$^{-1}$$. If the wave speed is 330 m s$$^{-1}$$, the frequency heard by the running person shall be close to:

Charge is distributed within a sphere of radius $$R$$ with a volume charge density $$\rho(r) = \frac{A}{r^2}e^{-\frac{2r}{a}}$$, where $$A$$ and $$a$$ are constants. If $$Q$$ is the total charge of this charge distribution, the radius $$R$$ is:

Two point charges $$q_1(\sqrt{10}$$ $$\mu$$C) and $$q_2(-25$$ $$\mu$$C) are placed on the $$x$$-axis at $$x = 1$$ m and $$x = 4$$ m respectively. The electric field (in V/m) at a point $$y = 3$$ m on $$y$$-axis is, [Take $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$C$$^{-2}$$]

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $$K_1$$, $$K_2$$, $$K_3$$, $$K_4$$ arranged as shown in the figure. The effective dielectric constant $$K$$ will be:

A carbon resistance has a following colour code. What is the value of the resistance?

GOY Golden

In the given circuit the internal resistance of the 18V cell is negligible. If $$R_1 = 400$$ $$\Omega$$, $$R_3 = 100$$ $$\Omega$$ and $$R_4 = 500$$ $$\Omega$$ and the reading of an ideal voltmeter across $$R_4$$ is 5 V, then the value of $$R_2$$ will be:

A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron $$= 1.6 \times 10^{-19}$$ C)

One of the two identical conducting wires of length $$L$$ is bent in the form of a circular loop and the other one into a circular coil of $$N$$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop $$(B_L)$$ to that at the centre of the coil $$(B_C)$$, i.e. $$\frac{B_L}{B_C}$$ will be:

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is 90%, the output current would be:

A series AC circuit containing an inductor (20 mH), a capacitor (120 $$\mu$$F) and a resistor (60 $$\Omega$$) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is:

The energy associated with electric field is $$(U_E)$$ and with magnetic field is $$(U_B)$$ for an electromagnetic wave in free space. Then:

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $$(M_1)$$ and parallel to the second mirror $$(M_2)$$ is finally reflected from the second mirror $$(M_2)$$ and parallel to the first mirror $$(M_1)$$. The angle between the two mirrors will be:

In a young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $$\lambda = 500$$ nm is incident on the slits. The total number of bright fringes that are observed in the angular range $$-30^{\circ} \leq \theta \leq 30^{\circ}$$ is:

The magnetic field associated with a light wave is given, at the origin, by $$B = B_0 [\sin(3.14 \times 10^7)ct + \sin(6.28 \times 10^7)ct]$$. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photoelectrons? ($$c = 3 \times 10^8$$ m s$$^{-1}$$, $$h = 6.6 \times 10^{-34}$$ J s)

At a given instant, say $$t = 0$$, two radioactive substance A and B have equal activities. The ratio $$\frac{R_B}{R_A}$$ of their activities after time $$t$$ itself decays with time $$t$$ as $$e^{-3t}$$. If the half-life of A is $$\ln 2$$, the half-life of B is:

Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of $$V_0$$ changes by: (assume that the Ge diode has large breakdown voltage)

In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width 6 MHz are (Take velocity of light $$c = 3 \times 10^8$$ m/s, $$h = 6.6 \times 10^{-34}$$ J-s)

The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is: