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.
Assertion (A): The gravitational force between two finite bodies is necessarily along the line joining their centre of mass.
Reason (R): The gravitational force between two particles is not central.
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 false.
The gravitational force between two finite bodies is generally not directed along the line joining their centers of mass.
Reason (R) is also false. The gravitational force between two point particles is always central, acting along the line connecting them. Therefore, both (A) and (R) are false.
Assertion (A): If the law of gravitation, instead of being inverse square law then planets will still have elliptical orbits.
Reason (R): In that case also, \( T^2 \propto r^3 \) (symbols having usual meanings)
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 false. Only an inverse-square force leads to stable, closed elliptical orbits. An inverse cube law would lead to unstable orbits. Reason (R) is also false. Kepler's third law, \( T^2 propto r^3 \), is a direct consequence of the inverse-square law. If the law changes, this relation no longer holds. Therefore, both (A) and (R) are false.
Assertion (A): Gravitational potential energy of any mass particle may not be zero at earth centre.
Reason (R): Gravitational field intensity at earth centre is zero.
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. Gravitational potential at the center of a uniform solid sphere is finite (e.g., \( -\frac{3}{2} \frac{GM}{R} \)), hence potential energy is non-zero. Reason (R) is true. Due to symmetry, the net gravitational field at the Earth's center is zero. However, zero field does not directly explain non-zero potential energy. Thus, (R) is not the correct explanation of (A).
Assertion (A): If the product of surface area and density is same for two planets, escape velocities at surface will be same for both planets.
Reason (R): For given mass of a planet \( v_e \propto R^{-1/2} \)
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.
Escape velocity \( v_e = \sqrt{\frac{2GM}{R}} \). Substitute \( M = \rho \frac{4}{3} \pi R^3 \) to get \( v_e = \sqrt{\frac{8G\pi R^2 \rho}{3}} \). If \( R^2 \rho \) is constant (derived from \( A\rho \) being constant), then \( v_e \) is constant. Reason (R) is true, as \( v_e = \sqrt{\frac{2GM}{R}} \) shows \( v_e \propto R^{-1/2} \) for constant \( M \). However, (R) does not explain (A), as the conditions are different.
Assertion (A): When planet moves in elliptical orbit around Sun. Its angular momentum about sun remains conserved.
Reason (R): Total mechanical energy of planet – sun system remains conserved.
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. Gravitational force is a central force, so the torque about the Sun is zero, leading to angular momentum conservation. Reason (R) is also true. Gravitational force is conservative, so total mechanical energy of the system is conserved. However, energy conservation does not explain angular momentum conservation, as they are distinct conservation laws.
Assertion (A): Moon revolving around earth does not come closer despite earth’s gravitational attraction.
Reason (R): A radially outward force balances earth’s force of attraction during revolution of moon.
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. The Moon maintains a stable orbit around Earth. Reason (R) is false. There is no radially outward force balancing Earth's gravity. Instead, Earth's gravitational force *is* the centripetal force required for the Moon's orbit. The Moon's tangential velocity prevents it from falling directly into Earth while gravity pulls it in.
Assertion (A): If earth stops rotating about its axis, then the value of acceleration due to gravity increases everywhere, except at the poles.
Reason (R): The value of acceleration due to gravity is maximum at the poles.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A): The effective gravity is given by \(g' = g - Romega^2cos^2lambda\). If \(omega = 0\), then \(g' = g\). This causes \(g\) to increase everywhere except at poles (where \(coslambda = 0\)). So (A) is true.nReason (R): Due to rotation and equatorial bulge, \(g\) is maximum at poles and minimum at the equator. So (R) is true.n(R) correctly explains (A) as the effect of rotation explains the variation.
Assertion (A): Even when orbit of a satellite is elliptical, its plane of rotation passes through the centre of earth.
Reason (R): According to law of conservation of angular momentum plane of rotation of satellite always remain same.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A): For any central force, the orbit is always planar and contains the center of force (Earth's center). So (A) is true.
Reason (R): Gravitational force is a central force, so net torque is zero. This implies conservation of angular momentum, \(\vec{L} = \vec{r} \times \vec{p}\), which means the orbital plane is fixed. So (R) is true. (R) correctly explains (A).
Assertion (A): The radius vector from the sun to a planet sweeps out equal areas in equal times interval.
Reason (R): Transverse (perpendicular to radius vector) acceleration of the planet is zero.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A): This statement is Kepler's Second Law, which is a direct consequence of angular momentum conservation. So (A) is true.nReason (R): For a central force, like gravity, the force acts along the radius vector, meaning no transverse force component exists. Thus, transverse acceleration is zero. So (R) is true.n(R) explains (A) because zero transverse acceleration leads to conservation of angular momentum, which implies Kepler's Second Law.