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Assertion : Generally the path of a proj...

Assertion : Generally the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to very great height.
Reason : Up to ordinary height the projectile moves under a uniform gravitational force, but for great heights, projectile moves under a variable force.

A

If both assertion and reason are true and reason is the correct explanation of assertion

B

If both assertion and reason are true but reason is not the correct explanation of assertion

C

If assertion is true but reason is false

D

If both assertion and reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Understand the Assertion The assertion states that the path of a projectile from the Earth is generally parabolic, but it becomes elliptical when the projectile reaches very great heights. 1. **Projectile Motion Basics**: In normal projectile motion (like a ball thrown), the path is parabolic due to the constant acceleration of gravity acting downwards. 2. **Great Heights**: At very high altitudes, the effects of gravity begin to change because the distance from the Earth's center increases significantly. **Conclusion for Step 1**: The assertion is true because at ordinary heights, the projectile follows a parabolic trajectory, while at great heights, the trajectory can become elliptical. ### Step 2: Understand the Reason The reason states that up to ordinary heights, the projectile moves under a uniform gravitational force, but at great heights, the projectile moves under a variable force. 1. **Uniform Gravitational Force**: Near the Earth's surface, gravitational force can be considered constant (approximately 9.81 m/s²). 2. **Variable Gravitational Force**: As the projectile ascends to great heights, the gravitational force decreases with the square of the distance from the Earth's center (according to Newton's law of gravitation). This means that the gravitational force is no longer uniform. **Conclusion for Step 2**: The reason is also true because the gravitational force changes with height, leading to different projectile paths. ### Step 3: Relationship Between Assertion and Reason Now we need to determine if the reason correctly explains the assertion. 1. **Explanation Validity**: The reason explains why the path changes from parabolic to elliptical as the height increases. The change in gravitational force is the key factor that influences the trajectory. 2. **Conclusion**: Since both the assertion and the reason are true, and the reason correctly explains the assertion, we can conclude that the statement is valid. ### Final Answer Both the assertion and the reason are true, and the reason correctly explains the assertion.
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Understand the Assertion The assertion states that the path of a projectile from the Earth is generally parabolic, but it becomes elliptical when the projectile reaches very great heights. 1. **Projectile Motion Basics**: In normal projectile motion (like a ball thrown), the path is parabolic due to the constant acceleration of gravity acting downwards. 2. **Great Heights**: At very high altitudes, the effects of gravity begin to change because the distance from the Earth's center increases significantly. ...
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