A uniform block of mass M slides on a smooth horizontal bar. Another mass
m is connected to it by an inextensible string of length / of negligible mass,
and is constrained to oscillate in the X-Y plane only. Neglect the sizes of the
masses. The number of degrees of freedom of the system is two and the
generalized coordinates are chosen as x and 0, as shown in the figure.
1
0-
m
vY
If Px and Po are the generalized momenta corresponding to x and e,
respectively, then the correct options) is(are)
(A) Px = (m + M)x + ml cos @ 0
(B) Po = ml2 - ml cos 0*
(C) Px is conserved
(D) Pe is conserved
Options:
(A) Px = (m + M)x + ml cos @ 0
(B) Po = ml2 - ml cos 0*
(C) Px is conserved
(D) Pe is conserved
Official Answer Key:
A, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.54 / PH Q.44)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Molecular Spectroscopy* (`Rotational Spectra of Diatomic Molecules & Rigid Rotator`) | **Section**: *Section 6: Atomic and Molecular Physics*
- **Question Type**: **MSQ** | **Marks**: **2 Marks** | **Negative Marks**: **0**
- **Governing Principles**: Solved directly by applying fundamental laws of **Molecular Spectroscopy**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **A, C**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.