NTA JEE Main 1st September 2021 Shift 2

The average translational kinetic energy of $$N_2$$ gas molecules at _________ °C becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt.
(Given $$k_B = 1.38 \times 10^{-23}$$ J K$$^{-1}$$) (Fill the nearest integer).

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 km h$$^{-1}$$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is _________ $$\times 10^5$$ N m$$^{-1}$$.

When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time $$T$$. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it takes time $$\alpha T$$, where $$\alpha$$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $$\frac{1}{\sqrt{x}} \cdot \frac{\alpha^2-1}{\alpha^2}$$ where $$x$$ = _________.

A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in the vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of the rod when it passes through its lowest position is _________ m s$$^{-1}$$.
(Take $$g = 10$$ m s$$^{-2}$$)

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is $$x : 4$$ where $$x$$ is _________.

A uniform heating wire of resistance 36 $$\Omega$$ is connected across a potential difference of 240 V. The wire is then cut into half and a potential difference of 240 V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 : $$x$$, where $$x$$ is _________.

A steel rod with $$y = 2.0 \times 10^{11}$$ N m$$^{-2}$$ and $$\alpha = 10^{-5}$$ °C$$^{-1}$$ of length 4 m and area of cross-section 10 cm$$^2$$ is heated from 0°C to 400°C without being allowed to extend. The tension produced in the rod is $$x \times 10^5$$ N where the value of $$x$$ is _________.

The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0°C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $$\frac{x}{10}$$. Then the value of $$x$$ (round off to the nearest integer) is _________.
(Given R = 8.31 J $$mol^{-1}$$ $$K^{-1}$$)

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is $$2 \times 10^3$$ km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $$\frac{\pi}{x}$$ rad h$$^{-1}$$, where $$x$$ is _________.

A carrier wave with amplitude of 250 V is amplitude modulated by a sinusoidal base band signal of amplitude 150 V. The ratio of minimum amplitude to maximum amplitude for the amplitude modulated wave is 50 : $$x$$, then value of $$x$$, is _________.