NTA JEE Main 24th February 2021 Shift 2

The period of oscillation of a simple pendulum is $$T = 2\pi\sqrt{\frac{L}{g}}$$. Measured value of $$L$$ is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of $$g$$ will be:

A particle is projected with velocity $$v_0$$ along $$x$$-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. $$ma = -\alpha x^2$$. The distance at which the particle stops:

A circular hole of radius $$\frac{a}{2}$$ is cut out of a circular disc of radius $$a$$ as shown in figure. The centroid of the remaining circular portion with respect to point O will be:

A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
[Use $$g = \frac{GM}{R^2} = 9.8$$ m s$$^{-2}$$ and radius of earth, $$R = 6400$$ km.]

If one mole of an ideal gas at $$(P_1, V_1)$$ is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $$(B \to C)$$. Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net work done by the gas is equal to:

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

In the given figure, a body of mass $$M$$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $$k$$, the frequency of oscillation of given body is:

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

Which of the following equations represents a travelling wave?

Two electrons each are fixed at a distance 2d. A third charge proton placed at the midpoint is displaced slightly by a distance $$x (x \ll d)$$ perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency:
($$m$$ = mass of charged particle)