Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Classical Mechanics Lagrange & Hamilton’s Canonical Equations
Assume that a particle of mass m is constrained to move on the hyperbola xy = b under gravity g, with b being a non-zero constant; here x is the horizontal direction and y is the vertical direction.
Which of the following is Lagrange's equation of motion?
1
\(m \ddot{x}\left(1+\frac{b^2}{x^4}\right)-2 \frac{b^2 m}{x^5} \dot{x}^2-\frac{m g b}{x^2}\) = 0
2
\(m \ddot{x}\left(1+\frac{b^2}{x^3}\right)-2 \frac{b^2 m}{x^5} \dot{x}^2-\frac{m g b}{x^2}\) = 0
3
\(m \ddot{x}\left(1+\frac{b^2}{x^4}\right)-2 \frac{b^2 m}{x^2} \dot{x}^2-\frac{m g b}{x^2}\) = 0
4
\(m \ddot{x}\left(1+\frac{b^2}{x^5}\right)-2 \frac{b^2 m}{x^3} \dot{x}^2-\frac{m g b}{x^2}\) = 0
5
Question Not Attempted