NTA JEE Main 2nd September 2020 Shift 1

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be:

Train A and train B are running on parallel tracks in the opposite directions with speed of 36 km hour$$^{-1}$$ and 72 km hour$$^{-1}$$, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km hour$$^{-1}$$. Speed (in m s$$^{-1}$$) of this person as observed from train B will be close to: (take the distance between the tracks as negligible)

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola $$y = 4Cx^2$$ and rotating with angular speed $$\omega$$ (see figure). The value of $$\omega$$ is (neglect friction):

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre 'O' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:

In a reactor, 2 kg of $$_{92}U^{235}$$ fuel is fully used up in 30 days. The energy released fission is 200 MeV. Given that the Avogadro number, $$N = 6.023 \times 10^{26}$$ per kilo mole and $$1 \; eV = 1.6 \times 10^{-19}$$ J. The power output of the reactor is close to:

A particle of mass m with an initial velocity $$u\hat{i}$$ collides perfectly elastically with a mass 3m at rest. It moves with a velocity $$v\hat{j}$$ after collision, then, v is given by:

Shown in the figure is a rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass 'm' and has another weight of mass 2m hung at a distance of 75 cm from A. The tension in the string at A is:

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $$\omega$$ rad s$$^{-1}$$. The difference in the height, h (in cm) of liquid at the Centre of vessel and at the sides of the vessel will be:

The mass density of a spherical galaxy varies as $$\frac{K}{r}$$ over a large distance $$r$$ from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is: