A particle moves in the x-y plane with velocity 𝐯 = aî + btĵ. At the instant t = a√3/b the magnitude of radial acceleration is b/n, find n = ?
Physics · Mixed Chapter
JEE Mains

Question

A particle moves in the x-y plane with velocity 𝐯 = aî + btĵ. At the instant t = a√3/b the magnitude of radial acceleration is b/n, find n = ?

G1 Physics · Accepted Answer

Step 1: Velocity is v=aî+btĵ, so acceleration is dv/dt=bĵ. Step 2: The component of acceleration perpendicular to the velocity (normal/radial acceleration of the path) is a⊥=|v×a|/|v| =ab/√(a²+b²t²). Step 3: At t=a√3/b, denominator =√(a²+3a²)=2a, so a⊥=b/2. Step 4: Since a⊥=b/n, n=2. Answer: 2.