Daily NEET MCQ- May 6, 2022 - NEET MCQ

The kinetic energy of a particle in SHM is given by:
0.5mA²w²cos²(wt + a), where a is the phase constant.
cos²(wt + a) = (1 + cos2(wt+a))/2.
Therefore the time period of oscillation of kinetic energy is 4/2 = 2s.

Let x = Asin(wt).
∴ Kinetic energy = 1/2 mA²w²cos²(wt)
potential energy = 1/2kA²sin²(wt).
According to given condition:
1/2mA²w²cos²(wt) = 1/2A²w²sin²(wt)
using, k = mw², we get:
tan²(wt) = 1.
∴ wt = π/4.
∴ x = Asin(π/4) = A/√2.

Let x = Asin(wt).
U = kA²sin²(wt)
K = 1/2mA²w²cos²(wt).
Given: U = 1/3K.
kA²sin²(wt) = (1/3)*(1/2)mA²w²cos²(wt),
and k = mw².
∴ tan²(wt) = 1/6. Or tan(wt) = 1/√6.
∴ sin(wt) = 1/√7.
x = Asin(wt) = A/√7.

1/2ka² = 8 & 1/2kb² = 18.
We have to find value of 1/2k(a + b) ².
∴ 1/2k(a + b)² = 8 + 18 + kab
= 26+(k*4*6/k)
= 26 + 24 = 50J.

In sublimation, the solid substance transforms directly to the vapor state without entering into the liquid state. This helps in separating sublimable compounds from non-sublimable ones. Whereas the other three, i.e. crystallization, distillation and differential extraction are used when a suitable solvent is involved. In other words, they deal with mainly liquids and not solids alone.

The process of distillation is based on the difference in the boiling points of the liquids. This is because, liquids having different boiling points vaporize at different temperatures. In this way, the vapors cooled can be collected separately from the liquid formed. Crystallization is used to separate volatile liquids from non-volatile liquids as well.

A seperatory funnel is used in differential extraction. Differential extraction involves separating the immiscible organic compound from the aqueous solvent. The separating funnel aids in this process of separating immiscible liquids. It also helps in layer formation, with the denser solvent at the bottom and the other on top. This layer formation is important for the process, and thus, separatory funnel is chosen as the apparatus for differential extraction.

Plants obtain most of their carbon and most of their oxygen from CO₂ in the atmosphere. However, their remaining nutritional requirements are obtained from water and minerals in the soil.

Most minerals enter the root by active absorption into the cytoplasm of epidermal cells. This needs energy in the form of ATP. Some ions also move into the epidermal cells passively.

Unloading of mineral ions which are required by the plants for growth and development occur at the fine vein endings through diffusion and active uptake by the plant cells.