NTA JEE Main 8th January 2020 Shift 2 - Physics

A simple pendulum is being used to determine the value of gravitational acceleration $$g$$ at a certain place. The length of the pendulum is 25.0 cm and a stopwatch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is:

A particle of mass $$m$$ and charge $$q$$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $$v$$ on the distance $$x$$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)

A particle moves such that its position vector $$\vec{r}(t) = \cos\omega t\,\hat{i} + \sin\omega t\,\hat{j}$$ where $$\omega$$ is a constant and $$t$$ is time. Then which of the following statements is true for the velocity $$\vec{v}(t)$$ and acceleration $$\vec{a}(t)$$ of the particle:

As shown in figure. When a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre of mass of remaining (shaded part of sphere is at G, i.e., on the surface of the cavity. R can be determined by the equation:

A particle of mass $$m$$ is dropped from a height $$h$$ above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $$\sqrt{2gh}$$. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $$\sqrt{\frac{h}{g}}$$ is

A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm s$$^{-1}$$. Its kinetic energy is:

Two liquids of densities $$\rho_1$$ and $$\rho_2$$ ($$\rho_2 = 2\rho_1$$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):

A Carnot engine having an efficiency of $$\frac{1}{10}$$ is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at a lower temperature is

Consider a mixture of $$n$$ moles of helium gas and $$2n$$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $$\frac{C_P}{C_V}$$ value will be:

A transverse wave travels on a taut steel wire with a velocity of $$v$$ when tension in it is $$2.06 \times 10^4$$ N. When the tension is changed to T, the velocity changed to $$\frac{v}{2}$$. The value of T is close to:

Consider two charged metallic spheres $$S_1$$ and $$S_2$$ of radii $$R_1$$ and $$R_2$$, respectively. The electric fields $$E_1$$ (on $$S_1$$) and $$E_2$$ (on $$S_2$$) on their surfaces are such that $$\frac{E_1}{E_2} = \frac{R_1}{R_2}$$. Then the ratio $$V_1$$ (on $$S_1$$)/$$V_2$$ (on $$S_2$$) of the electrostatic potentials on each sphere is:

A capacitor is made of two square plates each of side 'a' making a very small angle $$\alpha$$ between them, as shown in figure. The capacitance will be close to:

A galvanometer having a coil resistance 100 $$\Omega$$ gives a full scale deflection when a current of 1 mA is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of 10 V?

A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic field at the center of circle is:

As shown in the figure, a battery of emf $$\varepsilon$$ is connected to an inductor L and resistance R in series. The switch is closed at $$t = 0$$. The total charge that flows from the battery, between $$t = 0$$ and $$t = t_c$$ ($$t_c$$ is the time constant of the circuit) is:

A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by $$\vec{B} = 5 \times 10^{-8}\hat{j}$$ T. The corresponding electric field $$\vec{E}$$ is (speed of light = $$3 \times 10^8$$ m s$$^{-1}$$)

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by (Graphs are drawn schematically and are not to scale)

In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is $$\frac{1}{8}$$th of a wavelength. The ratio of the intensity of light at that point to that at the center of a bright fringe is:

An electron (mass m) with initial velocity $$\vec{v} = v_0\hat{i} + v_0\hat{j}$$ is in an electric field $$\vec{E} = -E_0\hat{k}$$. If $$\lambda_0$$ is initial de-Broglie wavelength of electron, its de-Broglie wave length at time $$t$$ is given by:

In the given circuit, value of Y is:

A ball is dropped from the top of a 100 m high tower on a planet. In the last $$\frac{1}{2}$$ s before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in m s$$^{-2}$$) near the surface on that planet is

An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth) from the centre of the earth, it has a speed of 12 km s$$^{-1}$$. Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km s$$^{-1}$$)? Give your answer to the nearest integer in km s$$^{-1}$$

Three containers $$C_1$$, $$C_2$$ and $$C_3$$ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process)

The value of $$\theta$$ (in $$^\circ$$C to the nearest integer) is__________

The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20 $$\Omega$$ and 5 $$\Omega$$, is connected to the parallel combination of two resistors 30 $$\Omega$$ and x $$\Omega$$. The voltage difference across the battery of internal resistance 20 $$\Omega$$ is zero, the value of x (in $$\Omega$$) is

The first member of the Balmer series of hydrogen atom has a wavelength of 6561 $$\mathring{A}$$. The wavelength of the second member of the Balmer series (in nm) is