NTA JEE Main 3rd September 2020 Shift 2

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

A particle is moving unidirectional on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale):

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m s$$^{-1}$$ in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m s$$^{-2}$$. Assume there is no rotational motion and loss of energy after the collision is negligible.]

A uniform rod of length '$$\ell$$' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $$\omega$$ the rod makes an angle $$\theta$$ with it (see figure). To find $$\theta$$ equate the rate of change of angular momentum (direction going into the paper) $$\frac{m\ell^2}{12}\omega^2 \sin\theta$$ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces $$F_H$$ and $$F_v$$ about the CM. The value of $$\theta$$ is then such that:

The mass density of a planet of radius R varies with the distance r from its centre as $$\rho(r) = \rho_0\left(1 - \frac{r^2}{R^2}\right)$$. Then the gravitational field is maximum at:

A metallic sphere cools from 50°C to 40°C in 300 s. If atmospheric temperature around is 20°C, then the sphere's temperature after the next 5 minutes will be close to:

A calorimeter of water equivalent 20 g contains 180 g of water at 25°C. 'm' grams of steam at 100°C is mixed in it till the temperature of the mixture is 31°C. The value of 'm' is close to (Latent heat of water = 540 cal g$$^{-1}$$, specific heat of water = 1 cal g$$^{-1}$$°C$$^{-1}$$)

To raise the temperature of a certain mass of gas by 50°C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100°C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $$fA$$. The value of $$f$$ is: