Gravitational Field

Practice Questions:

Question 1: easy

Two identical spheres each of mass M and radius R are separated by a centre to centre distance 10R. The gravitational force on mass m placed at the midpoint of the line joining the centres of the spheres is :

1. zero

2. 2GMm/25R²

3. GMm/25R²

4. GMm/100R²

View Answer

At the midpoint, the gravitational forces exerted by the two identical spheres on the mass \( m \) have the same magnitude but act in opposite directions. Since these forces cancel each other out completely, the net gravitational force on the mass \( m \) is:

\[
F = 0
\]

💬 Discuss this Question

Question 2: easy

A spherical shell has mass \(M\) and radius \(R\). A point mass \(m/2\) kept inside the shell at a distance \(R/2\) from centre. Then force of attraction on the mass is:

1. \(\frac{2Gm^2}{R^2}\)

2. \(\frac{Gm^2}{R^2}\)

3. \(\frac{Gm^2}{2R}\)

4. zero

View Answer

According to shell theorem, the gravitational field inside a uniform spherical shell is zero at all points. Thus, the force acting on the point mass is zero.

💬 Discuss this Question

Question 3: easy

The gravitational field in a region is given by \(vec{I} = 10(\hat{i} + \hat{j})\text{ N/kg}\). The work done by gravitational field to shift a particle of mass \(2\text{ kg}\) from position \((0,0)\) to \((5, 4)\) will be :

1. \(100\text{ J}\)

2. \(180\text{ J}\)

3. \(80\text{ J}\)

4. \(20\text{ J}\)

View Answer

The force is \(\vec{F} = mvec{I} = 2 \times 10(\hat{i} + \hat{j}) = 20\hat{i} + 20\hat{j}\text{ N}\). Displacement is \(\vec{d} = 5\hat{i} + 4\hat{j}\text{ m}\). Work done \(W = \vec{F} \cdot \vec{d} = (20)(5) + (20)(4) = 180\text{ J}\).

💬 Discuss this Question

Question 4: easy

Statement A: If a particle is outside a uniform spherical shell or solid sphere with a spherically symmetric internal mass distribution, the sphere attracts the particle.

Statement B: If a particle is inside a uniform spherical shell, the gravitational force on the particle is zero.

Statement C: If a particle is inside a uniform solid sphere, the gravitational force on the particle is zero.

In light of above statements choose the correct option.

1. Only statement C is correct

2. Only statements A and B are correct

3. Only statements C and B are correct

4. Only statements A and C are correct

View Answer

Statements A and B are correct (shell theorem). Inside a uniform solid sphere, the gravitational force is non-zero (except at the center) and varies linearly with distance from the center.

💬 Discuss this Question

Question 5: easy

Assertion (A): Gravitational field of a uniform spherical shell outside it is same as that of particle of same mass placed at its centre of mass.

Reason (R): For the calculation of gravitational force between any two uniform spherical shells, they can always be replaced by particles of same mass placed at respective centres.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Assertion (A) is true as per Newton's Shell Theorem, a uniform spherical shell behaves like a point mass at its center for external points. Reason (R) is also true and is the basis for simplifying calculations of gravitational forces between spherical objects. Hence, (R) correctly explains (A).

💬 Discuss this Question

Question 6: easy

Assertion (A): The force of attraction between a hollow spherical shell of uniform density and a point mass situated out side is just as if the entire mass of the shell is concentrated at the centre of the shell.

Reason (R): Gravitational forces caused by the various regions of the shell have components along the line joining the point mass to the centre as well as along a direction perpendicular to this line.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Assertion (A) is true, it's a direct consequence of Newton's Shell Theorem. Reason (R) is false because, by symmetry, the perpendicular components of gravitational forces from various regions of a uniform spherical shell cancel out, resulting in a net force purely along the line joining the point mass to the center. Therefore, (A) is true but (R) is false.

💬 Discuss this Question

Question 7: easy

Statement A: If a particle is outside a uniform spherical shell or solid sphere with a spherically symmetric internal mass distribution, the sphere attracts the particle.

Statement B: If a particle is inside a uniform spherical shell, the gravitational force on the particle is zero.

Statement C: If a particle is inside a uniform solid sphere, the gravitational force on the particle is zero.nIn light of above statements choose the correct option.

1. Only statement C is correct

2. Only statements A and B are correct

3. Only statements C and B are correct

4. Only statements A and C are correct

View Answer

By shell theorems, the gravitational force inside a uniform spherical shell is zero (Statement B is correct) and outside it behaves like a point mass (Statement A is correct). Inside a solid sphere, the force is non-zero (Statement C is incorrect).

💬 Discuss this Question

Question 8: easy

Assertion (A): A spherically symmetric shell produces no gravitational field anywhere.

Reason (R): The field due to various mass elements cancel out, everywhere for a spherically symmetric shell.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

A spherically symmetric shell produces zero gravitational field *inside* itself, but a non-zero field *outside*. Thus, "anywhere" and "everywhere" make both Assertion (A) and Reason (R) are false.

💬 Discuss this Question