NTA JEE Main 7th January 2020 Shift 2 - Physics

Given, $$B$$ is magnetic field induction, and $$\mu_0$$ is the magnetic permeability of vacuum. The dimension of $$\frac{B^2}{2\mu_0}$$ is:

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s$$^2$$) must be at least:

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45$$^\circ$$ with the vertical. Then F equals: (Take g = 10 m s$$^{-2}$$ and the rope to be massless)

Mass per unit area of a circular disc of radius a depends on the distance r from its centre as $$\sigma(r) = A + Br$$. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:

A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms$$^{-2}$$ at the north pole and the radius of the earth = 6400 km):

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecules changes from $$\tau_1$$ to $$\tau_2$$. If $$\frac{C_p}{C_v} = \gamma$$ for this gas then a good estimate for $$\frac{\tau_2}{\tau_1}$$ is given by

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, T$$_1$$ and T$$_2$$. The temperature of the hot reservoir of the first engine is T$$_1$$ and the temperature of the cold reservoir of the second engine is T$$_2$$. T is temperature of the sink of first engine which is also the source for the second engine. How is T related to T$$_1$$ and T$$_2$$, if both the engines perform equal amount of work?

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is $$v_0 = 1400$$ Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to:

A particle of mass $$m$$ and charge $$q$$ has an initial velocity $$\vec{v} = v_0 \hat{j}$$. If an electric field $$\vec{E} = E_0 \hat{i}$$ and magnetic field $$\vec{B} = B_0 \hat{i}$$ act on the particle, its speed will double after a time

In a building there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main supply is 220 V. The minimum fuse capacity (rated value) of the building will be:

In the figure, potential difference between A and B is:

The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are

The electric field of a plane electromagnetic wave is given by $$\vec{E} = E_0 \frac{\hat{i}+\hat{j}}{\sqrt{2}}\cos(kz + \omega t)$$. At $$t = 0$$, a positively charged particle is at the point $$(x, y, z) = \left(0, 0, \frac{\pi}{k}\right)$$. If its instantaneous velocity at $$(t = 0)$$ is $$v_0 \hat{k}$$, the force acting on it due to the wave is:

A planar loop of wire rotates in a uniform magnetic field. Initially, at $$t = 0$$, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

An emf of 20 V is applied at time $$t = 0$$ to a circuit containing in series 10 mH inductor and 5 $$\Omega$$ resistor. The ratio of the currents at time $$t = \infty$$ and at $$t = 40$$ s is close to: (Take $$e^2 = 7.389$$)

A thin lens made of glass (refractive index = 1.5) of focal length $$f = 16$$ cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $$f_l$$, then the ratio $$f_l/f$$ is closest to the integer:

In a Young's double slit experiment, the separation between the slits is 0.15 mm. In the experiment, a source of light of wavelength 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is:

An electron (of mass $$m$$) and a photon have the same energy $$E$$ in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vacuum)

The activity of a radioactive sample falls from 700 s$$^{-1}$$ to 500 s$$^{-1}$$ in 30 minutes. Its half life is close to:

The sum of two forces $$\vec{P}$$ and $$\vec{Q}$$ is $$\vec{R}$$ such that $$|\vec{R}| = |\vec{P}|$$. Find the angle between resultant of $$2\vec{P}$$ and $$\vec{Q}$$, and $$\vec{Q}$$,________

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is $$\mu = 0.4$$, the maximum possible value of $$100 \times \frac{b}{a}$$ for a box not to topple before moving is

M grams of steam at 100$$^\circ$$C is mixed with 200g of ice at its melting point in a thermally insulated container. If it produces liquid water at 40$$^\circ$$C [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g], the value of M is

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ)

The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 $$\Omega$$ is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the cell is $$\frac{n}{10}$$ $$\Omega$$, where n is an integer then value of n is