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A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror?
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A plane mirror is tied to the free end of an ideal spring. The other e...
Problem: A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror?
Solution:
To solve the problem, we need to analyze the motion of the mirror and the object before their collision.
Motion of Mirror:
When the spring is at its natural length, the mirror is moving with a constant speed V with respect to ground. The motion of the mirror can be analyzed as follows:
Motion of Object:
The object is moving towards the mirror with a constant velocity 2V with respect to ground. The motion of the object can be analyzed as follows:
Matching:
Before the collision of the object with the mirror, the following can be matched:
Solution:
To solve the problem, we need to analyze the motion of the mirror and the object before their collision.
Motion of Mirror:
When the spring is at its natural length, the mirror is moving with a constant speed V with respect to ground. The motion of the mirror can be analyzed as follows:
- At the equilibrium position, the net force on the mirror is zero, as the spring force balances the weight of the mirror.
- When the mirror is displaced from its equilibrium position, the spring exerts a restoring force on it, trying to bring it back to the equilibrium position.
- As the mirror moves towards its equilibrium position, its speed decreases and becomes zero at the equilibrium position.
- As the mirror moves beyond its equilibrium position, the spring force changes direction and tries to bring the mirror back towards the equilibrium position.
- Thus, the mirror oscillates about its equilibrium position with a constant amplitude and a frequency determined by the spring constant and the mass of the mirror.
- However, in this problem, the motion of the mirror is restricted to one dimension only, as it can slide freely along the smooth floor.
Motion of Object:
The object is moving towards the mirror with a constant velocity 2V with respect to ground. The motion of the object can be analyzed as follows:
- The object has a constant velocity of 2V with respect to ground, which is directed towards the mirror.
- As the object approaches the mirror, it will see its image in the mirror, which will appear to be moving towards it with a velocity of 2V.
- The image of the object will be located behind the mirror, at a distance equal to its actual distance from the mirror.
- As the object collides with the mirror, it will rebound with the same velocity and direction, as the mirror is assumed to be a perfect reflector.
- The image of the object will also rebound with the same velocity and direction, but it will be located behind the mirror, at a distance equal to its actual distance from the mirror.
Matching:
Before the collision of the object with the mirror, the following can be matched:
- The mirror is moving with a velocity V with respect to ground.
- The object is moving towards the mirror with a velocity of 2V with respect to ground.
- The image of the object is located behind the mirror, at a distance equal to its actual distance from the mirror.
- The image of the object is moving towards the object with a velocity of 2V.
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A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror?
Question Description
A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror?.
A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror?.
Solutions for A plane mirror is tied to the free end of an ideal spring. The other end of the spring is attached to a wall. The spring with mirror is held vertically to the smooth floor and it can side freely. when spring is at its natural length, the mirror is found to be moving at a speed V with respect to(w.r.t) ground. An object is moving towards the mirror with constant velocity 2V with respect to ground as shown. Match the following before collision of abject with mirror? in English & in Hindi are available as part of our courses for JEE.
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