Universal Law of Gravitation - NEET Free MCQ Test with solutions

The correct answer is Option C - Directly proportional to the product of their masses and inversely proportional to the square of the distance between them

The magnitude of the gravitational force between two point masses m₁ and m₂ separated by a distance r is given by F = G m₁ m₂ / r².

Here G is the gravitational constant with approximate value 6.67 × 10^-11 N m² kg^-2.

From the formula, the force is directly proportional to the product of the masses, so F ∝ m₁ m₂; for example, doubling one mass doubles the force.

The force is inversely proportional to the square of the distance, so F ∝ 1 / r²; for example, doubling r reduces the force to one quarter.

In vector form the force is attractive along the line joining the masses: ⃗F = -G m₁ m₂ / r² r̂, the negative sign indicating attraction toward the other mass.

These proportionalities and the formula confirm that Option C correctly states the dependence of gravitational force on the masses and separation.

The correct answer is Option A - 6.67 × 10^-11 N m² kg^-2

F = G m₁ m₂ / r² is the mathematical form of the universal law of gravitation, where G is the constant of proportionality.

Rearranging gives G = F r² / (m₁ m₂), so the SI units of G follow from the units of force, distance and mass.

Thus [G] = N · m² · kg^-2, which matches the unit shown in the correct option.

The experimentally determined numerical value in SI units is approximately 6.67 × 10^-11, so the full SI expression is 6.67 × 10^-11 N m² kg^-2.

The correct answer is Option D - 6.67 × 10⁻⁵ N

F = G \t m1 \t m2 / r²

Given G = 6.67 × 10^-11 N m² kg^-2, m₁ = 100 kg, m₂ = 10000 kg, r = 1 m.

m₁ · m₂ = 100 × 10000 = 1000000

Substituting, F = 6.67 × 10^-11 × 1000000 / 1² = 6.67 × 10^-5 N

Hence the magnitude of the gravitational force is 6.67 × 10⁻⁵ N, which matches the stated option.

Topic in NCERT: Universal law of gravitation

Line in NCERT: "newton's law of universal gravitation states that the gravitational force of attraction between any two particles of masses m₁ and m₂ separated by a distance r has the magnitude f = g(m₁m₂/r²)."

The correct answer is Option C - One-fourth of the original value

According to Newton's law of universal gravitation, the magnitude of the force between two point masses is given by

F = G m₁ m₂ / r²

For a new separation r' = 2r, the gravitational force becomes

F' = G m₁ m₂ / (r')²

F' = G m₁ m₂ / (2r)² = G m₁ m₂ / (4 r²)

Since F = G m₁ m₂ / r², it follows that F' = F / 4.

Therefore the gravitational force becomes one-fourth of the original value, confirming Option C.

The correct answer is Option A - A, C and D only

Statement A is true because gravitational force between two masses is always attractive; two masses always attract each other under classical gravity.

Statement B is false because gravitational interaction depends on the masses involved and their separation, not on the material medium; gravity acts through vacuum as well as through matter.

Statement C is true since a central force is one that acts along the line joining two bodies and depends only on their separation; gravitational force meets both conditions.

Statement D is true because the magnitude of gravitational force follows an inverse-square law.

F = G m₁ m₂ / r²

Statement E is false; gravity is the weakest of the fundamental interactions, much weaker than the electromagnetic and strong nuclear forces.

The correct answer is Option C - M^-1 L³ T^-2

Using the law of gravitation between two point masses, F = G m₁ m₂ / r².

The dimensional symbol of force is [F] = M L T^-2.

The dimensional symbols of mass and distance are [m] = M and [r] = L, respectively.

Rearranging the relation to find G gives [G] = [F][r]² / [m]².

Substituting dimensions: [G] = (M L T^-2)(L²)/(M²).

Simplifying yields [G] = M^-1 L³ T^-2, which matches Option C.

The correct answer is Option B - (A)-(II), (B)-(I), (C)-(III), (D)-(IV)

F = G m₁ m₂ / r²

• A → (II): The magnitude of the quantity represented by A varies as 1/r², so it obeys the inverse square law; its direction is along the line joining the bodies.

• B → (I): The symbol G is a universal constant; its measured value is 6.67×10^-11 N m² kg^-2, and it appears in the law shown above.

• C → (III): The quantity represented by C is a vector; it is defined as force per unit mass and has both magnitude and direction. g = F / m

• D → (IV): The quantity represented by D is a scalar; it has magnitude only and, for a point mass, is given by the expression below. V = - G M / r

The correct answer is Option C - 16 times the original force

According to Newton's law of gravitation, the force is given by F = G m₁ m₂ / r², where G is the gravitational constant.

Both masses are doubled, so they become 2 m₁ and 2 m₂, and the distance is halved to r/2.

The new force is F' = G (2 m₁)(2 m₂) / (r/2)².

Simplifying, the numerator gives 4 m₁ m₂ and the denominator is r²/4, so F' = G (4 m₁ m₂) / (r²/4).

Thus F' = 4 × 4 × (G m₁ m₂ / r²) = 16 F, i.e., the force becomes 16 times the original value.

The correct answer is Option B - Both statements are correct but Statement II does not explain Statement I

Statement I is true because, in classical gravity, the force depends only on the masses involved and their separation; the intervening material does not change the gravitational interaction between the masses.

F = G m₁ m₂ / r²

In the formula above, G is the gravitational constant, and m₁, m₂ and r are the two masses and the distance between them; none of these quantities is altered by placing a medium between the masses, and classical gravity has no shielding, so the force is independent of the medium.

Statement II is also true because the gravitational force between two point masses is directed along the line of the relative position vector; for extended bodies with spherical symmetry, the shell theorem shows the net force is as if the entire mass were concentrated at the centre, so the direction is along the line joining their centres.

Statement II gives the direction of the force but does not address the dependence (or independence) on the intervening medium; independence follows from the dependence on masses, distance and G, not from the force's direction.

Statement II does not explain Statement I. Therefore Option B is correct.

The correct answer is Option C - √3 × G × m² / a²

Each of the other two masses exerts a gravitational force of magnitude Gm²/a² on the chosen mass.

The two forces are symmetrically placed with an angle of 60° between them.

For two equal forces F with angle θ between them, the resultant magnitude is R = 2F cos(θ/2).

Here F = Gm²/a² and θ = 60°, so cos(θ/2) = cos30° = √3/2.

R = 2 × (Gm²/a²) × (√3/2)

R = √3 × Gm²/a²

Thus the magnitude of the resultant gravitational force equals √3 × G × m² / a², which corresponds to Option C.

The correct answer is Option D - 8F / 3

Using Newton's law of gravitation, the force is given by F = G m₁ m₂ / r².

One mass is increased by 50%, so it becomes 1.5 m₁ (= 3/2 m₁), and the separation is reduced to 75% of original, so r' = 0.75 r (= 3/4 r).

The new force is F' = G (1.5 m₁) m₂ / (0.75 r)².

Taking the ratio with the original force, F'/F = (3/2) / (3/4)².

Evaluating, (3/2) / (9/16) = (3/2) × (16/9) = 8/3, so F' = (8/3) F.

Therefore the new force equals 8F / 3, which matches Option D.

The correct answer is Option A - A, B and D only

• Weakest fundamental force: Gravitational interaction is far weaker than the other fundamental forces (strong, electromagnetic, weak); this is why it is described as the weakest fundamental force.

• Conservative force: The work done by gravity between two points is independent of the path taken, so the gravitational force is conservative. For any closed path, the net work by gravity is zero.

• Short-range - not true: gravity acts over arbitrary distances and is a long-range force, decreasing with distance but never becoming exactly zero.

  F = G m₁ m₂ / r²

  This inverse-square dependence shows that gravitational influence extends indefinitely, though it weakens with increasing r.

• Principle of superposition: Gravitational forces from multiple masses add vectorially; the net gravitational force is the vector sum of individual forces, so the principle of superposition holds.

• Can be shielded - not true: there is no known material or method that blocks or shields gravity; gravitational effects cannot be screened in the way electromagnetic fields can, so gravity is effectively unshieldable.

Option C is correct: the smaller body moves 7.5R before collision.

Let the smaller mass be m₁ = M and the larger mass be m₂ = 5M. The centres touch when their separation equals R + 2R = 3R, so the reduction in separation is 12R - 3R = 9R.

Let the displacement of the smaller mass towards the larger be Δx₁ and that of the larger mass towards the smaller be Δx₂. Because no external force acts, the centre of mass is fixed, giving the relation m₁Δx₁ = m₂Δx₂.

With m₁ = M and m₂ = 5M, this yields Δx₁ = 5Δx₂.

The total approach is Δx₁ + Δx₂ = 9R. Substituting gives 5Δx₂ + Δx₂ = 9R, so 6Δx₂ = 9R and Δx₂ = 1.5R.

Therefore Δx₁ = 5 × 1.5R = 7.5R. Hence the smaller body travels 7.5R before collision, corresponding to Option C.

The correct answer is Option B - Statement I is incorrect but Statement II is correct

The law of universal gravitation gives the force between two point masses as F = G m₁ m₂ / r², directed along the line joining them, where G is the gravitational constant.

Statement I is incorrect because the law itself is universal and applies to every pair of mass elements; the simple closed form F = G m₁ m₂ / r² is valid directly only for point masses or when an extended body is spherically symmetric and the force on an external point can be treated as if the entire mass were concentrated at the centre.

Statement II is correct because, for an extended body, the total gravitational force is obtained by the principle of superposition by summing (integrating) contributions of all mass elements. For a point mass m interacting with a continuous mass distribution with density ρ(r'), a differential force is dF = G m·dm / r² (with vector direction along the line joining the elements), and the net force is found by integrating over the body's volume.

In vector form, for a point at position r acted on by a continuous distribution ρ(r'), the force can be written as F = G m ∫ ρ(r') (r' - r) / |r' - r|³ dV', which implements the required integration over all mass elements.

Therefore, the correct assessment is that the first statement is false while the second statement is true, so Option B is correct.

The correct answer is Option D - 4 : 1

According to Newton's law of gravitation, the gravitational force between two point masses is given by F = G M m / r².

Let the force at the first distance be F₁ = G M m / r².

At twice the distance the force is F₂ = G M m / (2r)² = G M m / 4 r².

Therefore, the ratio F₁ : F₂ = (G M m / r²) : (G M m / 4 r²) which simplifies to 4 : 1.