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A block with mass M is conn ected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x = x0 + A. In both the cases, a particle with mass m(<M) is  softly placed on the block after which they stick to each other. Which of the following statement(s) is (are) true about the motion after the mass m is placed on the mass M?
  • a)
    The amplitude of oscillation in the first case chan ges by a factor of  whereas in the second case it remains unchanged.
  • b)
    The final time period of oscillation in both the cases is same.
  • c)
    The total energy decreases in both the cases.
  • d)
    The  instantaneous speed at x0 of the combined masses decreases in both the cases
Correct answer is option 'A,B,D'. Can you explain this answer?
Verified Answer
A block with mass M is conn ected by a massless spring with stiffness ...
Case (i) : Applying conservation of linear momentum.
 


Clearly E2 < E1
The new time Period 
Case (ii) : The new time Period 
Also A2 = A1
Here E2 = E1
The instantaneous value of speed at Xo of the combined masses decreases in both the cases.
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A block with mass M is conn ected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x = x0 + A. In both the cases, a particle with mass m(<M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is (are) true about the motion after the mass m is placed on the mass M?a)The amplitude of oscillation in the first case chan ges by a factor of whereas in the second case it remains unchanged.b)The final time period of oscillation in both the cases is same.c)The total energy decreases in both the cases.d)The instantaneous speed at x0 of the combined masses decreases in both the casesCorrect answer is option 'A,B,D'. Can you explain this answer?
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A block with mass M is conn ected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x = x0 + A. In both the cases, a particle with mass m(<M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is (are) true about the motion after the mass m is placed on the mass M?a)The amplitude of oscillation in the first case chan ges by a factor of whereas in the second case it remains unchanged.b)The final time period of oscillation in both the cases is same.c)The total energy decreases in both the cases.d)The instantaneous speed at x0 of the combined masses decreases in both the casesCorrect answer is option 'A,B,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A block with mass M is conn ected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x = x0 + A. In both the cases, a particle with mass m(<M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is (are) true about the motion after the mass m is placed on the mass M?a)The amplitude of oscillation in the first case chan ges by a factor of whereas in the second case it remains unchanged.b)The final time period of oscillation in both the cases is same.c)The total energy decreases in both the cases.d)The instantaneous speed at x0 of the combined masses decreases in both the casesCorrect answer is option 'A,B,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block with mass M is conn ected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x = x0 + A. In both the cases, a particle with mass m(<M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is (are) true about the motion after the mass m is placed on the mass M?a)The amplitude of oscillation in the first case chan ges by a factor of whereas in the second case it remains unchanged.b)The final time period of oscillation in both the cases is same.c)The total energy decreases in both the cases.d)The instantaneous speed at x0 of the combined masses decreases in both the casesCorrect answer is option 'A,B,D'. Can you explain this answer?.
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