On a horizontal plane, a projectile of mass m is launched from the ground with speed v0
at an angle đ0 with the horizontal. In addition to the gravitational force (mg), it also
experiences a drag force F drag = -đžv , where v is its velocity and đž is a constant. It hits
the ground at a distance R from the point of launch with its velocity making an angle
đ with the horizontal, as shown schematically in the figure. Then which of the following
options is correct?
Options:
(A) R = v0
2sin2đ
g đ < đ0
(B) R < v0
2sin2đ0
g đ < đ0
(C) R < v0
2sin2đ0
g đ > đ0
(D) R = v0
2sin2đ
g đ > đ0
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.16)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (1 Mark, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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