Gravitation Practice Questions - NDA Physics Question Bank

Question 1 of 10 Authentic UPSC NDA Question

What is the dimension of gravitational constant?

Step-by-Step Logic & Solution

Correct Answer

✓ Option [b] is correct. The gravitational constant \( G \) has the dimensions [M⁻¹L³T⁻²].

📖 Governing Law / Core Concept

The gravitational constant \( G \) is used in Newton's law of universal gravitation, which states:

\[ F = G \frac{m_1 m_2}{r^2} \]

where:

F = gravitational force between two masses (N)
G = gravitational constant (N m²/kg²)
m₁, m₂ = masses (kg)
r = distance between masses (m)

🧪 Step-by-Step Breakdown

From the formula: \[ F = G \frac{m_1 m_2}{r^2} \] we rearrange for \( G \): \[ G = \frac{F r^2}{m_1 m_2} \] Identifying SI units:

Force \( [F] \) = kg m/s²
Distance \( [r] \) = m
Mass \( [m] \) = kg

Substituting units into the equation:

\[ G = \frac{\text{kg m/s}^2 \cdot \text{m}^2}{\text{kg}^2} \]

Simplifying gives: \[ G = \frac{\text{kg} \cdot \text{m}^3/\text{s}^2}{\text{kg}^2} = \text{m}^3\text{kg}^{-1}\text{s}^{-2} \] Thus, the dimensional formula of \( G \) is:

\[ [G] = [M^{-1}L^{3}T^{-2}] \]

🔍 Option Analysis

Option A: [ML³T⁻²] - Incorrect, does not match dimensional derivation.
Option C: [M²L⁻²T⁻²] - Incorrect, does not match.
Option D: [M²L⁻¹T⁻²] - Incorrect, does not match.

⚡ Mnemonic / Speed-Run

Remember \( G = \frac{F r^2}{m_1 m_2} \) for deriving dimensions quickly. The negative exponents indicate inverse relationships.

6. Visual Suggestion

A schematic diagram illustrating the gravitational force between two masses, indicating distance \( r \) and the gravitational force \( F \), could enhance understanding. Show lines representing forces and labels for \( m_1 \) and \( m_2 \).

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XII Physics, Chapter 10 (Gravitation).

Question 2 of 10 Authentic UPSC NDA Question

T wo bodies of mass M each are placed R distance apart. In another system, two bodies of mass 2M each are placed R/2 distance apart. If F be the gravitational force between the bodies in the first system, then the gravitational force between the bodies in the second system will be

Step-by-Step Logic & Solution

Solution

Option (a) is correct.

Explanation:

\[ F = G \frac{m_1 m_2}{r^2} \]

For the first system: \[ F = G \frac{M \cdot M}{R^2} = G \frac{M^2}{R^2} \] For the second system with masses \(2M\) at distance \(\frac{R}{2}\): \[ F' = G \frac{(2M) \cdot (2M)}{\left(\frac{R}{2}\right)^2} = G \frac{4M^2}{\frac{R^2}{4}} = G \frac{4M^2 \cdot 4}{R^2} = G \frac{16M^2}{R^2} \] Now, relate \(F'\) to \(F\): \[ F' = 16 \times G \frac{M^2}{R^2} = 16F \] Thus, the gravitational force between the bodies in the second system is \(16F\).

📌 Hints / Properties Used:

Newton's Law of Universal Gravitation: \( F = G \frac{m_1 m_2}{r^2} \)
Force proportionality to mass and inverse square of distance

📊 Visual Diagram Suggestion:

A diagram depicting two sets of masses with labeled distances, showing F and F' clearly, with arrows indicating the direction and magnitude of gravitational forces.

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 11 (Gravitation)

Question 3 of 10 Authentic UPSC NDA Question

Suppose there are two planets 1 and 2, having the same density but radii R₁ and R₂ respectively, where R₁ > R₂. The accelerations due to gravity on the surfaces of these planets are related as

Step-by-Step Logic & Solution

Correct Answer

✓ Option (a) is correct. The gravitational acceleration is greater on the larger planet.

📖 Governing Law / Core Concept

The acceleration due to gravity (g) on the surface of a planet is given by the formula:

\[ g = \frac{GM}{R^2} \]

Where G is the gravitational constant, M is the mass of the planet, and R is its radius. For a planet of uniform density (ρ), mass can be expressed as:

\[ M = \frac{4}{3} \pi R^3 \rho \]

🧪 Step-by-Step Breakdown

Substituting the expression for mass into the equation for g:

\[ g = \frac{G \left( \frac{4}{3} \pi R^3 \rho \right)}{R^2} = \frac{4 \pi G \rho}{3} R \]

This indicates that g is directly proportional to the radius R when density is constant.

Let g₁ and g₂ be the gravitational accelerations on planets 1 and 2, respectively.

\[ g_1 = k \cdot R_1 \quad \text{and} \quad g_2 = k \cdot R_2 \]

Where k = \frac{4 \pi G \rho}{3}. Since R₁ > R₂, it follows that:

\[ g_1 > g_2 \]

📌 Hints / Properties Used:

Gravitational formula: \( g = \frac{GM}{R^2} \)
Relationship between mass, density, and volume
Proportionality of gravitational acceleration to radius in uniform density

📊 Visual Diagram Suggestion:

A diagram showing two planets with labeled radii R₁ and R₂, highlighting that R₁ > R₂. Arrows indicating greater gravitational pull g₁ compared to g₂ could aid in understanding.

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 10 (Gravitation).

Question 4 of 10 Authentic UPSC NDA Question

The correct sequence of energy transfer that occurs when an apple falls to the ground is

Step-by-Step Logic & Solution

Correct Answer

✓ Option (c) is correct. The energy transformation sequence is accurately captured.

📖 Governing Law / Core Concept

The falling apple demonstrates the Law of Conservation of Energy, which states that energy can neither be created nor destroyed; it merely transforms from one form to another.

🧪 Step-by-Step Breakdown

The energy transfer when the apple falls is as follows:

Gravitational Potential Energy (GPE): Initially, the apple possesses gravitational potential energy due to its height.
Kinetic Energy (KE): As the apple falls, GPE converts to kinetic energy, increasing its velocity.
Heat Energy to Air (Q_air): As the apple accelerates, it generates heat due to air friction.
Heat Energy to Ground and Apple (Q_ground): Upon hitting the ground, some kinetic energy is converted to heat, raising the temperature of both the apple and the ground.
Sound Energy: A portion of energy transforms into sound energy, which we hear upon the apple's impact.

🔍 Option Analysis

Option (a) incorrectly lists sound energy before heat energy transfers.
Option (b) fails to sequence kinetic energy after gravitational potential energy effectively.
Option (d) places sound energy before heat energy to the ground, which is inaccurate.

⚡ Mnemonic / Speed-Run

To remember the sequence: Gravity → Kinetic → Heat (air) → Heat (ground) → Sound can be abbreviated as GKHHs.

6. Visual Suggestion

A flowchart illustrating the sequential conversion of gravitational potential energy to kinetic energy, followed by heat energy transfer to air and ground, finally culminating in sound energy upon impact would be effective.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter on Work, Energy, and Power.

Question 5 of 10 Authentic UPSC NDA Question

Which one of the following is not a conservative force?

Step-by-Step Logic & Solution

Correct Answer

✓ Option (A) is correct. Frictional force is not a conservative force.

📖 Governing Law / Core Concept

A conservative force is defined as a force for which the work done is independent of the path taken and depends only on the initial and final positions. Mathematically, for a conservative force \( F \), the work done \( W \) can be expressed as:

\[ W = \int_{A}^{B} F \cdot dr \]

Where \( A \) and \( B \) are the initial and final points, \( dr \) is the displacement vector.

🧪 Step-by-Step Breakdown

In contrast, the frictional force is path-dependent, primarily arising from the interaction between surfaces. In any movement where friction is present, the work done against it will vary with the distance traveled:

\[ W_{\text{friction}} = -f \cdot d \]

Where \( f \) is the magnitude of the frictional force and \( d \) is the distance over which it acts.

🔍 Option Analysis

Electric Force: A conservative force where potential energy exists due to charge distribution.
Gravitational Force: A conservative force characterized by energy conservation in gravitational fields.
Spring Force: Another conservative force, described by Hooke's Law: \( F = -kx \), where \( k \) is the spring constant and \( x \) is the displacement.

⚡ Mnemonic / Speed-Run

Remember: "Conservative Forces Keep Their Path" - implies they depend only on endpoints.

6. Visual Suggestion

Illustrate a diagram showing the work done by conservative forces (electric, gravitational, spring) as path-independent, contrasting it with frictional force as path-dependent, highlighting the effect of distance traveled.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 6 (Work, Energy, and Power).

Question 6 of 10 Authentic UPSC NDA Question

Suppose, a ball of mass M is thrown upwards from a point A and it reaches up to the highest point B and returns back to point A, which one among the following is correct?

Step-by-Step Logic & Solution

Correct Answer

✓ Option (a) is correct. Kinetic Energy at A equals Potential Energy at B.

📖 Governing Law / Core Concept

The principle governing the motion of the ball is the Conservation of Mechanical Energy, which states that the total mechanical energy (sum of kinetic energy (KE) and potential energy (PE)) in a closed system remains constant if only conservative forces, like gravity, act on the body.

🧪 Step-by-Step Breakdown

As the ball is thrown upwards from point A:

At point A: Kinetic Energy is maximum, Potential Energy is minimum.
At point B (highest point): Velocity is zero, thus Kinetic Energy is zero, and Potential Energy is maximum.

By Conservation of Energy:

\[ KE_A + PE_A = KE_B + PE_B \]

Since \( PE_A = 0 \) (taking point A as reference), and \( KE_B = 0 \) (at highest point B), we have:

\[ KE_A = PE_B \]

Thus, at point B, the entire kinetic energy at A (when the ball was thrown) has been converted into potential energy.

🔍 Option Analysis

Option (b): Incorrect. Kinetic Energy at A is not equal to Potential Energy at A, as KE is maximum and PE is minimum there.
Option (c): Incorrect. At point B, KE is zero, whereas PE is maximum.
Option (d): Incorrect. At point B, KE is zero while at A it is maximum.

⚡ Mnemonic / Speed-Run

Remember: "Up is Potential, Down is Kinetic." Energy shifts from kinetic to potential as height increases.

6. Visual Suggestion

A schematic diagram illustrating the motion of the ball with labeled points A and B, showing kinetic energy decreasing as the ball rises and potential energy increasing, highlighting the energy transformation at the highest point.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 2 (Work, Energy, and Power).

Question 7 of 10 Authentic UPSC NDA Question

Which of the following statements withreference to L-Wave or Long Wave generatedby an earthquake is/are correct?

1. They follow the Earth’s circumference.

2. They travel at more or less at a constantrate.

Select the answer using the code given below:

Step-by-Step Logic & Solution

✓

1. Correct Answer

Option C is correct. Long Waves or L-Waves are surface seismic waves generated by earthquakes that follow the Earth's circumference and travel at a relatively constant rate.

📖 Short Explanation

Long Waves (L-Waves) are surface waves that travel along the Earth's surface, often following the curvature of the Earth, resulting in the majority of the earthquake’s damaging impact.

💡 3. Why Correct Answer is Correct

L-Waves (Long Waves) are a type of surface seismic wave, created by the energy from an earthquake as they move through the Earth’s outermost layer. These waves move along the Earth’s surface and can follow the curvature of the Earth, making them responsible for extensive damage during seismic events. L-Waves generally travel at a slower speed compared to body waves like P-Waves and S-Waves, but maintain a more consistent rate as they propagate through varied surface conditions. This constant rate depends on the media they travel through.

L-Wave Speed = Function of Ground Properties

❌ 4. Why Other Options are Wrong

•Option A: Incorrect because although they follow the Earth’s curvature, statement 2 is also true, making option A incomplete.
•Option B: While L-Waves do travel at a relatively constant rate, ignoring statement 1 about them following Earth's circumference makes this answer incomplete.
•Option D: This option is incorrect because both statements are actually correct; L-Waves follow the Earth's surface and travel at a more or less constant rate.

⚡

NDA Speed-Run / Mnemonic Shortcut

Remember “CLING” for Constant Long-waves that travel In a Never-ending loop on Ground. This mnemonic helps recall L-Waves as major surface waves moving around the Earth.

🎯

5. Key Learning Point

L-Waves, being surface-focused with a relatively consistent travel rate, are highly destructive due to their extensive reach along Earth's surface.

6. Visual Suggestion

Illustrate a cross-section of the Earth with annotated layers showing L-Waves moving along the surface to demonstrate how their trajectory follows the Earth's circumference. A side view of wave paths could clarify the wave movement along the curvature.

Question 8 of 10 Authentic UPSC NDA Question

Two bodies of unequal masses are dropped from a tower. At any instant, they have equal

Step-by-Step Logic & Solution

✓

1. Correct Answer

Option B is correct. Both bodies experience equal acceleration due to gravity.

📖 Core Concept

In free fall, all objects experience the same gravitational acceleration, which is approximately 9.8 m/s², irrespective of their mass.

💡 3. Explanation

When dropped from a height in a vacuum:

a = g = 9.8 m/s²

Both bodies will have the same acceleration throughout their fall.

❌ 4. Option Analysis

•Option A: Momentum is mass times velocity; thus, momentum varies due to differing masses.
•Option C: Potential energy differs because it depends on both height and mass.
•Option D: Kinetic energy is affected by mass and velocity; thus, it varies between the two bodies.

⚡

NDA Speed-Run / Mnemonic Shortcut

Remember: In free fall, all bodies accelerate at 9.8 m/s², independent of their mass.

🎯

5. Key Takeaways

In free fall, all objects experience equal acceleration due to gravity, regardless of mass.

6. Visual Suggestion

Illustrate a diagram depicting two bodies of different masses dropped from the same height, with arrows indicating gravitational force and equal acceleration vectors. Include labeled axes for clarity.

Question 9 of 10 Authentic UPSC NDA Question

The universal constant of gravitation G has the unit

Step-by-Step Logic & Solution

✓

1. Correct Answer

Option D is correct. The unit of the universal constant of gravitation G is N m²/kg².

📖 Core Concept

The gravitational constant G quantifies the strength of gravitational attraction between two masses, essential for Newton's law of gravitation.

💡 3. Explanation

The gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) at a distance \( r \) is given by:

\( F = \frac{G \cdot m_1 \cdot m_2}{r^2} \)

Rearranging gives:

\[ G = \frac{F \cdot r^2}{m_1 \cdot m_2} \]

Substituting units:

\[ [G] = \frac{N \cdot m^2}{kg^2} = N \cdot \frac{m^2}{kg^2} \]

❌ 4. Option Analysis

•Option A: N represents force, not gravitational constant.
•Option B: m/s is the unit of speed, not relevant for \( G \).
•Option C: Joule (J) is a unit of energy, which does not define \( G \).

⚡

NDA Speed-Run / Mnemonic Shortcut

Recall that \( G \) derives its units from the gravitational force equation, yielding N m²/kg².

🎯

5. Key Takeaways

The unit of the universal constant of gravitation \( G \) is N m²/kg², integral for calculating gravitational forces.

Question 10 of 10 Authentic UPSC NDA Question

The figure given below shows the direction ofthe two forces P and Q acting on a skydiver:QPWhich one of the following statements is correctabout the two forces?

Step-by-Step Logic & Solution

Correct Answer

✓ Option (c) is correct. After the parachute opens, force P remains the same, while force Q increases.

📖 Governing Law / Core Concept

According to Newton's Second Law of Motion, the net force acting on an object determines its motion. The forces P and Q signify gravitational pull and air resistance, respectively.

🧪 Step-by-Step Breakdown

Initially, the force due to gravity (P) is expressed as:

\[ P = mg \]

where \( m \) is the mass of the skydiver and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). The force due to air resistance (Q) can be given by:

\[ Q = \frac{1}{2} \rho v^2 C_d A \]

where \( \rho \) is the air density, \( v \) is the velocity, \( C_d \) is the drag coefficient, and \( A \) is the cross-sectional area. Upon opening the parachute, the area (A) increases, leading to an increase in resistance Q. Meanwhile, P remains unchanged as mass and gravitational acceleration do not change.

🔍 Option Analysis

Option A: Incorrect; P is gravity, Q indicates air resistance.
Option B: Incorrect; P must equal Q for constant velocity (not a condition here).
Option D: Incorrect; P remains constant while Q increases.

⚡ Mnemonic / Speed-Run

Remember: "Parachute opens, resistance grows!"

6. Visual Suggestion

A force diagram illustrating forces P (gravity) and Q (air resistance) acting on the skydiver, highlighting the change in Q when the parachute opens.

📖 Factual Verification & Reference:

Verified against NCERT Class XI Physics, Chapter 5 (Laws of Motion).

Gravitation Questions

Correct Answer

📖 Governing Law / Core Concept

🧪 Step-by-Step Breakdown

🔍 Option Analysis

⚡ Mnemonic / Speed-Run

6. Visual Suggestion

6. Visual Suggestion

📖 Factual Verification & Reference

Solution

Correct Answer

📖 Governing Law / Core Concept

🧪 Step-by-Step Breakdown

📌 Hints / Properties Used:

📊 Visual Diagram Suggestion:

Correct Answer

📖 Governing Law / Core Concept

🧪 Step-by-Step Breakdown

🔍 Option Analysis

⚡ Mnemonic / Speed-Run

6. Visual Suggestion

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

🧪 Step-by-Step Breakdown

🔍 Option Analysis

⚡ Mnemonic / Speed-Run

6. Visual Suggestion

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

🧪 Step-by-Step Breakdown

🔍 Option Analysis

⚡ Mnemonic / Speed-Run

6. Visual Suggestion

6. Visual Suggestion

📖 Factual Verification & Reference

1. Correct Answer

📖 Short Explanation

💡 3. Why Correct Answer is Correct

❌ 4. Why Other Options are Wrong

NDA Speed-Run / Mnemonic Shortcut

5. Key Learning Point

6. Visual Suggestion

1. Correct Answer

📖 Core Concept

💡 3. Explanation

❌ 4. Option Analysis

NDA Speed-Run / Mnemonic Shortcut

5. Key Takeaways

6. Visual Suggestion

1. Correct Answer

📖 Core Concept

💡 3. Explanation

❌ 4. Option Analysis

NDA Speed-Run / Mnemonic Shortcut

5. Key Takeaways

Correct Answer

📖 Governing Law / Core Concept

🧪 Step-by-Step Breakdown

🔍 Option Analysis

⚡ Mnemonic / Speed-Run

6. Visual Suggestion