NTA JEE Main 8th January 2020 Shift 2

A simple pendulum is being used to determine the value of gravitational acceleration $$g$$ at a certain place. The length of the pendulum is 25.0 cm and a stopwatch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is:

A particle of mass $$m$$ and charge $$q$$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $$v$$ on the distance $$x$$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)

A particle moves such that its position vector $$\vec{r}(t) = \cos\omega t\,\hat{i} + \sin\omega t\,\hat{j}$$ where $$\omega$$ is a constant and $$t$$ is time. Then which of the following statements is true for the velocity $$\vec{v}(t)$$ and acceleration $$\vec{a}(t)$$ of the particle:

As shown in figure. When a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre of mass of remaining (shaded part of sphere is at G, i.e., on the surface of the cavity. R can be determined by the equation:

A particle of mass $$m$$ is dropped from a height $$h$$ above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $$\sqrt{2gh}$$. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $$\sqrt{\frac{h}{g}}$$ is

A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm s$$^{-1}$$. Its kinetic energy is:

Two liquids of densities $$\rho_1$$ and $$\rho_2$$ ($$\rho_2 = 2\rho_1$$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):

A Carnot engine having an efficiency of $$\frac{1}{10}$$ is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at a lower temperature is

Consider a mixture of $$n$$ moles of helium gas and $$2n$$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $$\frac{C_P}{C_V}$$ value will be:

A transverse wave travels on a taut steel wire with a velocity of $$v$$ when tension in it is $$2.06 \times 10^4$$ N. When the tension is changed to T, the velocity changed to $$\frac{v}{2}$$. The value of T is close to: