A 15 cm long scale is held horizontally with one of its ends on the edge of a 1 m high table
and the other end resting on one's index finger. As the finger is removed (see figure below),
the scale starts rotating about its end on the table. After 0.1 s, during which it has rotated
by a negligibly small angle but has gained a rotational speed as it leaves the table and falls
vertically towards the ground. When its centre of mass has fallen by 0.5 m, it has rotated
by an angle 𝜃. The value of 𝜃 in degrees (rounded off to one decimal place) is _____
(g = 9.8 m.s-2)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.65)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Atomic & Molecular Physics** within *Section 6: Atomic and Molecular Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Atomic & Molecular Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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