Forces

Concept: Newton's Law of Universal Gravitation states that the gravitational force ( ) between two objects of masses and , separated by a distance between their centers, is given by: where is the gravitational constant. This formula shows that the force of gravitation is inversely proportional to the square of the distance between the objects ( ). Step 1: Write the initial force Let the initial distance between the two objects be . The initial gravitational force is: Step 2: Define the new distance The distance between them is reduced to half. Let the new distance be . So, . Step 3: Calculate the new force ( ) with the new distance The new gravitational force with distance is: Substitute : To simplify the fraction in the denominator, multiply the numerator by the reciprocal of , which is : Step 4: Relate the new force ( ) to the initial force ( ) We know from Step 1 that . Substituting this into the expression for : This means the new force is 4 times the initial force . So, when the distance is reduced to half, the force of gravitation becomes 4 times stronger. This matches option (2).

Concept: A force is an interaction that, when unopposed, will change the motion of an object. It can also deform an object. Mass is an intrinsic property of an object. Step 1: Understanding the effects of force According to Newton's Laws of Motion and general physics principles:
Change in Speed (4): A net force can cause an object to accelerate (Newton's Second Law, ). Acceleration is the rate of change of velocity. If velocity changes, its magnitude (speed) can change. For example, pushing a toy car can make it go faster.
Change in Direction (3): Force is a vector. If a force is applied in a direction different from the object's current motion, it can change the direction of motion. For example, a planet orbiting a star is constantly changing direction due to the gravitational force.
Change in Shape (1): Forces can cause deformation. If you squeeze a rubber ball or stretch a spring, its shape changes due to the applied force. Step 2: Considering mass Mass (2): Mass is a measure of the amount of matter in an object. In classical (non-relativistic) physics, the mass of an object is considered an intrinsic and constant property. Applying a force to an object does not change the amount of matter it contains. For example, if you push a 5 Kg box, its mass remains 5 Kg; it doesn't become 4 Kg or 6 Kg just because you pushed it. (Note: In relativistic physics, at very high speeds close to the speed of light, mass can increase. Also, in nuclear reactions, mass can be converted to energy. However, for typical scenarios implied by such a question, we assume classical physics where mass is constant unless matter is added or removed from the object.) Conclusion: A force can change an object's speed, direction of motion, and shape. However, applying a force does not change the object's mass. Therefore, force on an object cannot change its mass.