## RAHUL MEHLA is teaching live on Unacademy Plus

CLASSICAL MECHANICS SOLUTIONS GATE-2010 QI. For the set of all Lorentz transformations with velocities along the x-axis consider the two statements given below: P: If L is a Lorentz transformation then, L is also a Lorentz transformation Q: If L and L2 are Lorentz transformations then, LiL2 is necessarily a Loren transformation. Choose the correct option (A) P is true and Q is false (C) Both P and Q are false (B) Both P and Q are true (D) P is false and Q is true ns: (b)

A particle is placed in a region with the potential V(x)--kx2--3, where k, > x", where 2 en (A)r-0 and xare points of stable equilibrium (B)x-0 is a point of stable equilibrium and xis a point of unstable equilibrium (C) x-0 and x- are points of unstable equilibrium (D) There are no points of stable or unstable equilibrium

(D) There are no points of stable or unstable equilibrium Ans (b) Solution: V=-kx, 3 +ve (Stable) and Al x = ,-=-ve (unstable

Q3. A meson at rest decays into two photons, which move along the x-axis. They are both 10s. In an inertial frame moving with a velocity 6c in the direction of one of the photons, the time interval between the two detected simultaneously after a time, V 0. detections is (A) 15 s (B) 0 s (C) 10 s (D) 20 s Ans (a) 1+0.6 1-0.6 Solution: ,- 10 10x2 20sec t,t 1-0.6 10.6 tt15sec 10 10x-5sec