NTA JEE Main 7th January 2020 Shift 2

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