JEE Advanced 2016Paper 2
- Exam
- JEE Advanced
- Year
- 2016
- Paper
- Paper 2
- Subject
- Physics
- Chapter
- Oscillations
JEE Advanced 2016 · Paper 2 · Physics · Oscillations
A block with mass M is connected by a massless spring with...
A block with mass M is connected 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 . Consider two cases : (i) when the block is at and (ii) when the block is at In both the cases, a particle with mass 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?
Options
- AThe amplitude of oscillation in the first case changes by a factor of \sqrt{\dfrac{\text{M}}{\text{m} + {\text{M}}^{′}}} whereas in the second case it remains unchanged
- BThe final time period of oscillation in both the cases is same
- CThe total energy decreases in both the cases
- DThe instantaneous speed at of the combined masses decreases in both the cases.
Correct answer
A. The amplitude of oscillation in the first case changes by a factor of \sqrt{\dfrac{\text{M}}{\text{m} + {\text{M}}^{′}}} whereas in the second case it remains unchanged
Step-by-step solution
{\text{T}}_{\text{i}} = 2 π \sqrt{\dfrac{\text{M}}{\text{K}}} , {\text{T}}_{\text{f}} = 2 π \sqrt{\dfrac{\text{M} + \text{m}}{\text{K}}}
Case (i):
\text{M} \left(\text{A} ω\right) = \left(\text{M} + \text{m}\right) \text{V}
∴ Velocity decreases at equilibrium position.
By energy conservation
Case (ii):
No energy loss, amplitude remains same
At equilibrium \left({x}_{0}\right) velocity = \text{A} ω
In both cases ω decrease so velocity decreases in both cases
Case (i):
\text{M} \left(\text{A} ω\right) = \left(\text{M} + \text{m}\right) \text{V}
∴ Velocity decreases at equilibrium position.
By energy conservation
Case (ii):
No energy loss, amplitude remains same
At equilibrium \left({x}_{0}\right) velocity = \text{A} ω
In both cases ω decrease so velocity decreases in both cases