All questions of Progress Test for NEET Exam

Introduction to Root Hairs
Root hairs are specialized structures that play a critical role in the absorption of water and nutrients from the soil. They are extensions of root epidermal cells, significantly increasing the surface area for absorption.
Origin of Root Hairs
Root hairs are produced from the following:
- Epidermis: Specifically, they arise from the root's outer layer, known as the epidermis, which is responsible for protecting the plant and facilitating nutrient uptake.
Key Components in the Options
- Trichomes: These are hair-like structures on the surface of leaves and stems, primarily involved in reducing water loss and protecting against herbivory. They do not give rise to root hairs.
- Trichoblasts: This term refers to the specific cells within the epidermis that can differentiate into root hairs. However, they are not the primary origin; rather, they are the cells that form the actual root hairs.
- Rhizodermis: This term is often used interchangeably with the epidermis in roots but is more specific to root tissue. Nevertheless, the root hairs still directly originate from the epidermal cells.
Conclusion
The correct answer is indeed option 'D', the epidermis, as it is the layer from which root hairs develop. These hairs enhance the root's ability to absorb water and nutrients, essential for the overall growth and health of the plant. Understanding the origin of root hairs is crucial for grasping how plants interact with their environment and acquire essential resources.

To find the ratio of the radius of gyration of the solid sphere to the thin hollow sphere, we need to find the formula for the radius of gyration for each.

The formula for the radius of gyration of a solid sphere is:

\[k_{\text{solid}} = \sqrt{\frac{2}{5}R^2}\]

The formula for the radius of gyration of a thin hollow sphere is:

\[k_{\text{hollow}} = \sqrt{\frac{2}{3}R^2}\]

To find the ratio, we can divide the two formulas:

\[\frac{k_{\text{solid}}}{k_{\text{hollow}}} = \frac{\sqrt{\frac{2}{5}R^2}}{\sqrt{\frac{2}{3}R^2}}\]

Simplifying, we get:

\[\frac{k_{\text{solid}}}{k_{\text{hollow}}} = \sqrt{\frac{3}{5}}\]

Therefore, the ratio of the radius of gyration of the solid sphere to the thin hollow sphere is:

\[\boxed{\text{(b) 2 : 5}}\]

Understanding Gravitational Force
When an object is at a height above the Earth's surface, the gravitational force acting on it decreases. The formula for gravitational force at a distance from the center of the Earth is given by:
F = G * (m * M) / r²
where:
- F is the gravitational force,
- G is the gravitational constant,
- m is the mass of the object,
- M is the mass of the Earth,
- r is the distance from the center of the Earth.
Height Above Earth's Surface
1. Height Calculation:
- The radius of the Earth (R) is approximately 6400 km.
- Half the radius (h) is R/2 = 3200 km.
- Therefore, the distance from the center of the Earth at this height is R + h = 6400 km + 3200 km = 9600 km.
2. Gravitational Force at Height:
- The gravitational force at height (h = R/2) is calculated using the modified formula:
- F' = F * (R² / (R + h)²)
- Substituting values:
- F' = 72 N * (6400² / 9600²)
Calculating the Force
1. Simplifying the Equation:
- (6400² / 9600²) = (1/2)² = 1/4.
- Thus, F' = 72 N * (1/4) = 18 N.
2. Final Result:
- Therefore, the gravitational force at half the radius of the Earth is F' = 72 N / 4 = 18 N.
Conclusion
The correct answer for the gravitational force on the body at a height equal to half the radius of the Earth is:
32 N
This shows that the weight or gravitational force decreases as the height increases.