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A ball of mass m strikes the inclined face of the wedge normally with speed. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for (i) m as system, along (ii) M as system, along (iii) (M m) as system, along X (iv) (M m) as system, along Y Which of the following is correct?
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A ball of mass m strikes the inclined face of the wedge normally with ...
The conservation of momentum states that the total momentum of a closed system remains constant unless acted upon by an external force. In the event of a collision, the conservation of momentum can be applied to the system consisting of the colliding objects.
In the case described, a ball of mass m strikes the inclined face of a wedge at rest on a rough horizontal surface. The momentum of the ball before the collision is given by mv, where v is the speed of the ball. After the collision, the momentum of the ball and the wedge will be different, and the total momentum of the system consisting of the ball and the wedge will also be different.
The conservation of momentum can be applied to the event of collision for the following systems:
(i) m as a system, along the direction of motion of the ball before the collision.
(ii) M as a system, along the direction of motion of the ball before the collision.
(iii) (M m) as a system, along the x-axis (perpendicular to the direction of motion of the ball before the collision).
(iv) (M m) as a system, along the y-axis (perpendicular to the x-axis and the direction of motion of the ball before the collision).
Therefore, the correct answer is (i), (ii), (iii), and (iv) are all correct.
This question is part of UPSC exam. View all JEE courses
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A ball of mass m strikes the inclined face of the wedge normally with ...
Conservation of Momentum in a Collision of Ball and Wedge
The given problem involves a ball of mass m colliding with a wedge, which is at rest on a rough horizontal surface. We need to determine the applicability of the conservation of momentum for different systems during the collision.
Applicable System for Conservation of Momentum
(i) m as system: In this case, the system includes only the ball of mass m. Since there are no external forces acting on the system, the momentum of the ball remains conserved during the collision. However, the momentum of the wedge changes due to the collision, and hence, the conservation of momentum is not applicable for the entire system.
(ii) M as system: In this case, the system includes only the wedge of mass M. Since there are no external forces acting on the system, the momentum of the wedge remains conserved during the collision. However, the momentum of the ball changes due to the collision, and hence, the conservation of momentum is not applicable for the entire system.
(iii) (M+m) as system, along X: In this case, the system includes both the ball and the wedge. Since there are no external forces acting on the system along the horizontal direction, the momentum of the system remains conserved during the collision along the X-axis. However, the momentum of the system changes due to the collision along the Y-axis, and hence, the conservation of momentum is not applicable for the entire system.
(iv) (M+m) as system, along Y: In this case, the system includes both the ball and the wedge. Since there are no external forces acting on the system along the vertical direction, the momentum of the system remains conserved during the collision along the Y-axis. However, the momentum of the system changes due to the collision along the X-axis, and hence, the conservation of momentum is not applicable for the entire system.
Conclusion
From the above analysis, we can conclude that the conservation of momentum is applicable for the ball and wedge system only along the X-axis or Y-axis separately. However, it is not applicable for the entire system during the collision.
The given problem involves a ball of mass m colliding with a wedge, which is at rest on a rough horizontal surface. We need to determine the applicability of the conservation of momentum for different systems during the collision.
Applicable System for Conservation of Momentum
(i) m as system: In this case, the system includes only the ball of mass m. Since there are no external forces acting on the system, the momentum of the ball remains conserved during the collision. However, the momentum of the wedge changes due to the collision, and hence, the conservation of momentum is not applicable for the entire system.
(ii) M as system: In this case, the system includes only the wedge of mass M. Since there are no external forces acting on the system, the momentum of the wedge remains conserved during the collision. However, the momentum of the ball changes due to the collision, and hence, the conservation of momentum is not applicable for the entire system.
(iii) (M+m) as system, along X: In this case, the system includes both the ball and the wedge. Since there are no external forces acting on the system along the horizontal direction, the momentum of the system remains conserved during the collision along the X-axis. However, the momentum of the system changes due to the collision along the Y-axis, and hence, the conservation of momentum is not applicable for the entire system.
(iv) (M+m) as system, along Y: In this case, the system includes both the ball and the wedge. Since there are no external forces acting on the system along the vertical direction, the momentum of the system remains conserved during the collision along the Y-axis. However, the momentum of the system changes due to the collision along the X-axis, and hence, the conservation of momentum is not applicable for the entire system.
Conclusion
From the above analysis, we can conclude that the conservation of momentum is applicable for the ball and wedge system only along the X-axis or Y-axis separately. However, it is not applicable for the entire system during the collision.
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A ball of mass m strikes the inclined face of the wedge normally with speed. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for (i) m as system, along (ii) M as system, along (iii) (M m) as system, along X (iv) (M m) as system, along Y Which of the following is correct?
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A ball of mass m strikes the inclined face of the wedge normally with speed. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for (i) m as system, along (ii) M as system, along (iii) (M m) as system, along X (iv) (M m) as system, along Y Which of the following is correct? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A ball of mass m strikes the inclined face of the wedge normally with speed. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for (i) m as system, along (ii) M as system, along (iii) (M m) as system, along X (iv) (M m) as system, along Y Which of the following is correct? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of mass m strikes the inclined face of the wedge normally with speed. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for (i) m as system, along (ii) M as system, along (iii) (M m) as system, along X (iv) (M m) as system, along Y Which of the following is correct?.
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